Acceleration in quantum mechanics and electric charge quantization

In this study, we have discussed the implications of acceleration in quantum mechanics by means of a generalized derivative operator (GDO). A new Schrödinger equation is obtained which depends on the reduced Compton wavelength of the particle. We have discussed its implications in quantum mechanics for different types of potentials mainly the infinite wall potential, the gravitational linear field potential, the Cornell potential and the Coulomb repulsive potential. The corresponding wave functions and discrete energies are modified and differ from the results obtained in the conventional formalism. The major results obtained concerned the large improvement of the ground energy of the electron subject to the gravitational acceleration in addition to Cornell potential and the emergence of quantized electric charge in the theory without including Dirac monopoles or using gauge theories.

Measurement of hindered diffusion in complex geometries for high-speed studies of single-molecule forces

In a high-speed single-molecule experiment with a force probe, a protein is tethered between two substrates that are manipulated to exert force on the system. To avoid nonspecific interactions between the protein and nearby substrates, the protein is usually attached to the substrates through long, flexible linkers. This approach precludes measurements of mechanical properties with high spatial and temporal resolution, for rapidly exerted forces are dissipated into the linkers. Because mammalian hearing operates at frequencies reaching tens to hundreds of kilohertz, the mechanical processes that occur during transduction are of very short duration. Single-molecule experiments on the relevant proteins therefore cannot involve long tethers. We previously characterized the mechanical properties of protocadherin 15 (PCDH15), a protein essential for human hearing, by tethering an individual monomer through very short linkers between a probe bead held in an optical trap and a pedestal bead immobilized on a glass coverslip. Because the two confining surfaces were separated by only the length of the tethered protein, hydrodynamic coupling between those surfaces complicated the interpretation of the data. To facilitate our experiments, we characterize here the anisotropic and position-dependent diffusion coefficient of a probe in the presence of an effectively infinite wall, the coverslip, and of the immobile pedestal.

Modeling of the Van Der Waals Forces during the Adhesion of Capsule-Shaped Bacteria to Flat Surfaces

A novel model is developed to evaluate the van der Waals (vdW) interactions between a capsule shaped bacterium (P. putida) and flat minerals plates in different approach profiles: Vertically and horizontally. A comparison of the approaches to the well-developed spherical particle to mineral surface (semi-infinite wall and spherical) approach has been made in this investigation. The van der Waals (vdW) interaction potentials for a capsule-shaped bacterium are found using Hamaker’s microscopic approach of sphere to plate and cylinder to plate either vertically or horizontally to the flat surface. The numerical results show that a horizontal orientated capsule shaped bacterium to mineral surface interaction was more attractive compared to a capsule shaped bacterium approaching vertically. The orientation of the bacterial approaching a surface as well as the type and topology of the mineral influence the adhesion of a bacteria to that surface. Furthermore, the density difference among each type of bacteria shape (capsule, cylinder, and sphere) require different amounts of energy to adhere to hematite and quartz surfaces.

Measurement of hindered diffusion in complex geometries for high-speed single-molecule experiments

In a high-speed single-molecule experiment, a protein is tethered between two substrates that are manipulated to exert force on the system. To avoid nonspecific interactions between the protein and nearby substrates, the protein is usually attached to the substrates through long, flexible linkers. This approach precludes measurements of mechanical properties with high spatial and temporal resolution, for rapidly exerted forces are dissipated into the linkers. Because mammalian hearing operates at frequencies reaching tens to hundreds of kilohertz, the mechanical processes that occur during transduction are of very short duration. Single-molecule experiments on the relevant proteins therefore cannot involve long tethers. We previously characterized the mechanical properties of protocadherin 15 (PCDH15), a protein essential for human hearing, by tethering an individual monomer through very short linkers between a probe bead held in an optical trap and a pedestal bead immobilized on a glass coverslip. Because the two confining surfaces were separated by only the length of the tethered protein, hydrodynamic coupling between those surfaces complicated the interpretation of the data. To facilitate our experiments, we characterize here the anisotropic and position-dependent diffusion coefficient of a probe in the presence of an effectively infinite wall, the coverslip, and of the immobile pedestal.

One-dimensional quantum mechanics with Dunkl derivative

In this paper, we consider the quantum mechanics with Dunkl derivative. We use the Dunkl derivative to obtain the coordinate representation of the momentum operator and Hamiltonian. We introduce the scalar product to find that the momentum is Hermitian under this inner product. We study the one-dimensional box problem (the spin-less particle with mass m confined to the one-dimensional infinite wall). Finally, we discuss the harmonic oscillator problem.

Initial development of a free-surface wall jet at moderate Reynolds number

The steady laminar flow of a moderately inertial wall jet is examined theoretically near the exit of a channel. The free-surface jet emerges asymmetrically from the channel as it adheres to an infinite (upper) wall subject to a pressure gradient. The problem is solved using the method of matched asymptotic expansions. The small parameter involved in the expansions is the inverse cubic power of the Reynolds number. The flow field is obtained by matching the inviscid rotational core flow separately with the free-surface and the two wall layers. The upstream influence is examined as well as the break in the symmetry between the two wall layers. The wall jet exhibits a contraction near the channel exit that is independent of inertia, and eventually expands for any Reynolds number. Unlike the flow of a wall jet emerging into the same ambient fluid, the free-surface jet experiences a limited weakening in shear stress along the infinite wall, suggesting the possibility of separation for a jet with relatively low inertia. Significant shearing and elongation ensue at the exit, accompanied by flattening of the velocity profile near the upper wall.