Dc-Dc Buck-Boost Conversion

Van der Waals heterostructures are engineered materials composed of two or more different two-dimensional (2D) materials stacked together, relying on van der Waals forces for adhesion rather than covalent bonds. These heterostructures enable the combination of distinct electronic, optical, and mechanical properties, allowing for novel functionalities that cannot be achieved with individual materials. For instance, by stacking transition metal dichalcogenides (TMDs) with graphene, researchers can create devices with tunable band gaps and enhanced carrier mobility. The alignment of the layers can be precisely controlled, leading to the emergence of phenomena such as interlayer excitons and superconductivity. The versatility of van der Waals heterostructures makes them promising candidates for applications in next-generation electronics, photonics, and quantum computing.

The Coulomb Force is a fundamental force of nature that describes the interaction between electrically charged particles. It is governed by Coulomb's Law, which states that the force $F$ between two point charges $q_1$ and $q_2$ is directly proportional to the product of the absolute values of the charges and inversely proportional to the square of the distance $r$ between them. Mathematically, this is expressed as:

where $k$ is Coulomb's constant, approximately equal to $8.99 \times 10^9 \, \text{N m}^2/\text{C}^2$. The force is attractive if the charges are of opposite signs and repulsive if they are of the same sign. The Coulomb Force plays a crucial role in various physical phenomena, including the structure of atoms, the behavior of materials, and the interactions in electric fields, making it essential for understanding electromagnetism and chemistry.

Graphene-Based Field-Effect Transistors (GFETs) are innovative electronic devices that leverage the unique properties of graphene, a single layer of carbon atoms arranged in a hexagonal lattice. Graphene is renowned for its exceptional electrical conductivity, high mobility of charge carriers, and mechanical strength, making it an ideal material for transistor applications. In a GFET, the flow of electrical current is modulated by applying a voltage to a gate electrode, which influences the charge carrier density in the graphene channel. This mechanism allows GFETs to achieve high-speed operation and low power consumption, potentially outperforming traditional silicon-based transistors. Moreover, the ability to integrate GFETs with flexible substrates opens up new avenues for applications in wearable electronics and advanced sensing technologies. The ongoing research in GFETs aims to enhance their performance further and explore their potential in next-generation electronic devices.

Transcranial Magnetic Stimulation (TMS) is a non-invasive neuromodulation technique that uses magnetic fields to stimulate nerve cells in the brain. This method involves placing a coil on the scalp, which generates brief magnetic pulses that can penetrate the skull and induce electrical currents in specific areas of the brain. TMS is primarily used in the treatment of depression, particularly for patients who do not respond to traditional therapies like medication or psychotherapy.

The mechanism behind TMS involves the alteration of neuronal activity, which can enhance or inhibit brain function depending on the stimulation parameters used. Research has shown that TMS can lead to improvements in mood and cognitive function, and it is also being explored for its potential applications in treating various neurological and psychiatric disorders, such as anxiety and PTSD. Overall, TMS represents a promising area of research and clinical practice in modern neuroscience and mental health treatment.

Physics-Informed Neural Networks (PINNs) are a novel class of artificial neural networks that integrate physical laws into their training process. These networks are designed to solve partial differential equations (PDEs) and other physics-based problems by incorporating prior knowledge from physics directly into their architecture and loss functions. This allows PINNs to achieve better generalization and accuracy, especially in scenarios with limited data.

The key idea is to enforce the underlying physical laws, typically expressed as differential equations, through the loss function of the neural network. For instance, if we have a PDE of the form:

where $\mathcal{N}$ is a differential operator and $u(x,t)$ is the solution we seek, the loss function can be augmented to include terms that penalize deviations from this equation. Thus, during training, the network learns not only from data but also from the physics governing the problem, leading to more robust predictions in complex systems such as fluid dynamics, material science, and beyond.

The Hessian Matrix is a square matrix of second-order partial derivatives of a scalar-valued function. It provides important information about the local curvature of the function and is denoted as $H(f)$ for a function $f$. Specifically, for a function $f: \mathbb{R}^n \rightarrow \mathbb{R}$, the Hessian is defined as: