Barun Majumder

Motivated by generalized uncertainty principle, we derive a discrete picture of the space that respects Lorentz symmetry as well as gauge symmetry through setting an equivalency between linear GUP correction term and electromagnetic interaction term in Dirac equation. We derived a wavefunction solution that satisfies this equivalency. This discreteness may explain the crystal and quasicrystal structures observed in nature at different energy scales.

Cytotoxic T lymphocytes (CTLs) are important in controlling some viral infections, and therapies involving transfer of large numbers of cancer-specific CTLs have been successfully used to treat several types of cancers in humans. While molecular mechanisms of how CTLs kill their targets are relatively well understood we still lack solid quantitative understanding of the kinetics and efficiency at which CTLs kill their targets in different conditions. Collagen-fibrin gel-based assays provide a tissue-like environment for the migration of CTLs, making them an attractive system to study the cytotoxicity in vitro. Budhu et al. [1] systematically varied the number of peptide (SIINFEKL)- pulsed B16 melanoma cells and SIINFEKL-specific CTLs (OT-1) and measured remaining targets at different times after target and CTL co-inoculation into collagen-fibrin gels. The authors proposed that their data were consistent with a simple model in which tumors grow exponentially and are killed by CTLs at a per capita rate proportional to the CTL density in the gel. By fitting several alternative mathematical models to these data we found that this simple “exponential-growth-mass-action-killing” model does not precisely fit the data. However, determining the best fit model proved difficult because the best performing model was dependent on the specific dataset chosen for the analysis. When considering all data that include biologically realistic CTL concentrations ( E ≤ 10 ⁷ cell/ml) the model in which tumors grow exponentially and CTLs suppress tumor’s growth non-lytically and kill tumors according to the mass-action law (SiGMA model) fitted the data with best quality. Results of power analysis suggested that longer experiments (∼ 3 − 4 days) with 4 measurements of B16 tumor cell concentrations for a range of CTL concentrations would best allow to discriminate between alternative models. Taken together, our results suggest that interactions between tumors and CTLs in collagen-fibrin gels are more complex than a simple exponential-growth- mass-action killing model and provide support for the hypothesis that CTLs impact on tumors may go beyond direct cytotoxicity.

In this paper, we explore the black hole solutions with the rainbow deformed metric in the presence of the exponential form of the nonlinear electrodynamics with asymptotic Reissner- Nordstr ̈om properties. We calculate the exact solution of metric function and explore the geometri- cal properties in the background of massive gravity. From the obtained solution, the existence of the singularity is confirmed in proper limits. Using the solutions we also investigate the thermodynamic properties of the solutions by checking the validity of the first law of thermodynamics. Continuing the thermodynamic study, we investigate the conditions under which the system is thermally stable from the heat capacity and the Gibbs free energy. We also discuss the possible phase transition and the criticality of the system. It was found that the quantum gravitational effects of gravity’s rain- bow render the thermodynamic system stable in the vicinity of the singularity. Hence, we obtained a first order phase transition which is interpreted as the large/small black hole phase transition. From the equation of state it was found that after diverging at the singularity, the system evolves asymptotically into pressure-less dust as one moves away from the central singularity. We also calculated the quantum work using the change of the Helmholtz free energy.

In this paper, we analyze the correction to the mean field theory potential for a system of nucleons. It will be argued that these corrections can be obtained by deforming the Schrödinger’s equation describing a system of nucleons by a minimal length in the background geometry of space-time. This is because such a minimal length occurs due to quantum gravitational effects, and modifies the low energy quantum mechanical systems. In fact, as the mean field potential for the nucleons is represented by the Woods–Saxon potential, we will explicitly analyze such corrections to this potential. We will obtain the corrections to the energy eigenvalues of the deformed Schrödinger’s equation for the Woods–Saxon potential. We will also construct the wave function for the deformed Schrödinger’s equation.

In this paper, we analyze the correction to the mean field theory potential for a system of nucleons. It will be argued that these corrections can be obtained by deforming the Schr\"{o}dinger's equation describing a system of nucleons by a minimal length in the background geometry of space-time. This is because such a minimal length occurs due to quantum gravitational effects, and modifies the low energy quantum mechanical systems. In fact, as the mean field potential for the nucleons is represented by the Woods-Saxon potential, we will explicitly analyze such corrections to this potential. We will obtain the corrections to the energy eigenvalues of the deformed Schr\"{o}dinger's equation for the Woods-Saxon potential. We will also construct the wave function for the deformed Schr\"{o}dinger's equation.

In this paper, a two-dimensional analytical model of a laterally graded-channel triple-metal double-gate Junctionless Field Effect Transistor with hetero dielectric gate oxide stack consisting of SiO$_2$ and HfO$_2$ is derived. The model illustrates higher drive current and better performance against hazardous SCEs and HCEs in below 30 nm regime. Parabolic approximation method is used here to construct channel potentials and electric fields by solving 2-D Poisson's equation with applicable boundary conditions. The basic central and surface potentials as well as central and surface electric fields are being illustrated, Threshold voltage, DIBL, sub-threshold swing (SS) and a compact current model have also been deduced. These parameters clearly show the benefits of proposed graded-channel triple-metal double-gate structure with hetero-dielectric gate oxide stack. The device has reliability in low power applications because of its better Ion and Ioff control. Finally, the analytical model is validated with self-consistent numerical calculations to illustrate better performance of among available junctionless devices.

Various approaches to Quantum Gravity suggest an existence of a minimal measurable length. The cost to have such minimal length could be modified uncertainty principle, modified dispersion relation, non-commutative geometry or breaking of continuous Lorentz symmetry. In this paper, we propose that minimal length can be obtained naturally through spin–orbit interaction. We consider Dresselhaus anisotropic spin–orbit interaction as the perturbative Hamiltonian. When applied to a particle, it implies that the space, which seizes this particle, should be quantized in terms of units that depend on particle’s mass. This suggests that all measurable lengths in the space are quantized in units depending on existent mass and the Dresselhaus coupling constant. On one side, this indicates a breakdown of the space continuum picture near the scale of tabletop experiments, and on the other side, it proposes that spin–orbit interaction is a possible quantum gravity effect at low energy scale that leads naturally to space quantization.