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Lie group methods are applied to the time-dependent, monoenergetic neutron diffusion equation in materials with spatial and time dependence. To accomplish this objective, the underlying 2nd order partial differential equation (PDE) is…
We use interface-resolved simulations to study finite-size effects in turbulent channel flow of neutrally-buoyant spheres. Two cases with particle sizes differing by a factor of 2, at the same solid volume fraction of 20% and bulk Reynolds…
Polymer melts show a characteristic molecular weight dependent relaxation time that can be related to the unentangled and entangled regime. At high molecular weights, influence of contour length fluctuations and con-straint release cease…
We present a unified approach for qualitative and quantitative analysis of stability and instability dynamics of positive bright solitons in multi-dimensional focusing nonlinear media with a potential (lattice), which can be periodic,…
In the framework of potential models for heavy quarkonium the mass spectrum for the system ($\bar b c$) is considered. Spin-dependent splittings, taking into account a change of a constant for effective Coulomb interaction between the…
We demonstrate that the leading and next-to-leading finite-volume effects in the evaluation of leptonic decay widths of pseudoscalar mesons at $O(\alpha)$ are universal, i.e. they are independent of the structure of the meson. This is…
We propose a model for the quantum harmonic oscillator on a discrete lattice which can be written in supersymmetric form, in contrast with the more direct discretization of the harmonic oscillator. Its ground state is easily found to be…
The complex scaling method (CSM) is one of the most powerful methods of describing the resonances with complex energy eigenstates, based on non-Hermitian quantum mechanics. We present the basic application of CSM to the properties of the…
We study the properties of three-body resonances using a lattice complex scalar $\varphi^4$ theory with two scalars, with parameters chosen such that one heavy particle can decay into three light ones. We determine the two- and three-body…
Every linear system of partial differential equations (PDEs) admits a scaling symmetry in its dependent variables. In conjunction with other admitted symmetries of linear type, the associated invariant solution condition poses a linear…
The impact of confinement on self-assembly of particles interacting with short-range attraction and long-range repulsion (SALR) potential is studied for thermodynamic states corresponding to local ordering of clusters or layers in the bulk.…
We develop here a general formalism for multi-orbital Mott systems which can be used to understand dynamical and static spectral weight transfer. We find that the spectral weight transferred from the high energy scales is greatly increased…
A stochastic PDE, describing mesoscopic fluctuations in systems of weakly interacting inertial particles of finite volume, is proposed and analysed in any finite dimension $d\in\mathbb{N}$. It is a regularised and inertial version of the…
Classical and quantum dynamics of a harmonic oscillator in a monochromatic wave is studied in the exact resonance and near resonance cases. This model describes, in particular, a dynamics of a cold ion trapped in a linear ion trap and…
The multi-electron wave function of an interacting electron system depends on the size of the system, i.e. the number of electrons. Here the question investigated is how the wave function changes for a symmetric Friedel-Anderson impurity…
The equation of state of QCD matter at high densities is relevant for neutron star structure and for neutron star mergers and has been a focus of recent work. We show how lattice QCD simulations, free of sign problems, can provide an upper…
Molecular weight dependence of excluded volume effects is examined. The swollen-to-unperturbed coil transition point shifts to lower concentration range with increasing molecular weight (Mw). It is shown that in the limit of the infinite…
In this work, three different particle sizes: the static radius $R_{s}$, hydrodynamic radius $R_{h}$ and apparent hydrodynamic radius $ R_{h,app}$ obtained using the light scattering technique, are investigated for dilute poly-disperse…
Understanding the phase behavior of mixtures with many components is important in many contexts, including as a key step toward a physics-based description of intracellular compartmentalization. Here, we study the instabilities of a mixture…
Vector ($\Upsilon$) and pseudoscalar ($\eta_b$) bottonium ground states are studied at finite temperature in the framework of thermal Hilbert moment QCD sum rules. The mass, the onset of perturbative QCD in the complex squared energy plane,…