An efficient BEM for numerical solution of the biharmonic boundary value problem

This paper presents an efficient BEM for solving biharmonic equations. All boundary values including geometries are approximated by the universal high order radial basis function networks (RBFNs) rather than the usual low order interpolations. Numerical results show that the proposed BEM is considerably superior to the linear/quadratic-BEM in terms of both accuracy and convergence rate

Solving high-order partial differential equations with indirect radial basis function networks

This paper reports a new numerical method based on radial basis function networks (RBFNs) for solving high-order partial differential equations (PDEs). The variables and their derivatives in the governing equations are represented by integrated RBFNs. The use of integration in constructing neural networks allows the straightforward implementation of multiple boundary conditions and the accurate approximation of high-order derivatives. The proposed RBFN method is verified successfully through the solution of thin-plate bending and viscous flow problems which are governed by biharmonic equations. For thermally driven cavity flows, the solutions are obtained up to a high Rayleigh number

The t-t'-J model in one dimension using extremely correlated Fermi liquid theory and time dependent density matrix renormalization group

We study the one dimensional t-t'-J model for generic couplings using two complementary theories, the extremely correlated Fermi liquid theory and time-dependent density matrix renormalization group over a broad energy scale. The two methods provide a unique insight into the strong momentum dependence of the self-energy of this prototypical non-Fermi liquid, described at low energies as a Tomonaga-Luttinger liquid. We also demonstrate its intimate relationship to spin-charge separation, i.e. the splitting of Landau quasiparticles of higher dimensions into two constituents, driven by strong quantum fluctuations inherent in one dimension. The momentum distribution function, the spectral function, and the excitation dispersion of these two methods also compare well

The perceptions of pan-European advertising communication: a cross-cultural study between UK and Spain

One of the characteristics of globalisation is the increased level of standardisation in international marketing communications, and advertising in particular. As it has been a decade since the formation of European Union, it is imperative to re-assess how advertisements are perceived and consequently embraced in different nations, when audiences apparently have different cultural backgrounds. This cross cultural study compares UK and Spanish perceptions of 16 carefully selected advertisements, where their consequent perceptions and levels of recall were tested. A stratified sampling process was used to generate 150 UK and 150 Spanish audiences in a survey. The valid samples for analysis comprised of 298 cases. The results indicate that there is no significant difference in the levels of recall of the selected advertisements between the UK and Spanish audiences. Furthermore, evidence suggests that there is no significant difference in the way that the sample audience relate the advertisements to their own cultures. Nevertheless, the results revealed that there are significant differences in abilities of advertisement recall amongst different age groups, which suggest that some age groups are more prone to advertisement sensitivity than others. These results are encouraging for both academics and practitioners as the standardisation of pan-European advertising campaigns can be recognised as a viable option, and the economy of scales of advertising can be exploited

Liability for Deadly Failure: Rejecting the Push for PREP Act Preemption and Restraining PREP Act Immunity for Senior Living Facilities and Nursing Homes

In the wake of COVID-19, there has been a surge of wrongful death cases filed by plaintiff families in state courts. These families allege that their loved one contracted and died from COVID-19 because the nursing home or senior living facility at which their loved one resided failed to take proper COVID-19 prevention measures. In response, defendant facilities have removed these actions to federal court, arguing that the PREP Act preempts plaintiffs’ state law claims and grants facilities immunity from liability for loss related to qualified actions taken during a public health emergency. This Comment rejects facilities’ push for preemption which has been used as a tactic to stretch out litigation and to encourage plaintiff families to settle their cases for less. This Comment also encourages amendment of the PREP Act immunity laws to clarify that the Act does not preempt state law claims but does restrict senior living facilities and nursing homes from the privilege of immunity for loss resulting from a failure to act. Restraining immunity in this way will hold facilities accountable for their deadly failure to take COVID- 19 safety precautions and will incentivize facilities to take more stringent precautions when caring for their elderly residents in the future

Solution of two-center time-dependent Dirac equation in spherical coordinates: Application of the multipole expansion of the electron-nuclei interaction

A non-perturbative approach to the solution of the time-dependent, two-center Dirac equation is presented with a special emphasis on the proper treatment of the potential of the nuclei. In order to account for the full multipole expansion of this potential, we express eigenfunctions of the two-center Hamiltonian in terms of well-known solutions of the "monopole" problem that employs solely the spherically-symmetric part of the interaction. When combined with the coupled-channel method, such a wavefunction-expansion technique allows for an accurate description of the electron dynamics in the field of moving ions for a wide range of internuclear distances. To illustrate the applicability of the proposed approach, the probabilities of the K- as well as L- shell ionization of hydrogen-like ions in the course of nuclear alpha-decay and slow ion-ion collisions have been calculated

Non-equilibrium work fluctuations for oscillators in non-Markovian baths

We study work fluctuation theorems for oscillators in non-Markovian heat baths. By calculating the work distribution function for a harmonic oscillator with motion described by the generalized Langevin equation, the Jarzynski equality (JE), transient fluctuation theorem (TFT), and Crooks' theorem (CT) are shown to be exact. In addition to this derivation, numerical simulations of anharmonic oscillators indicate that the validity of these nonequilibrium theorems do not depend on the memory of the bath. We find that the JE and the CT are valid under many oscillator potentials and driving forces whereas the TFT fails when the driving force is asymmetric in time and the potential is asymmetric in position.Comment: 7 pages, 3 figure