Peri-personal Space

Simple and reproducible procedures are described for making three structurally distinct collagen assemblies from a common commercially available Type I collagen monomer. Native type, fibrous long spacing or segmental long spacing collagen can be constructed by varying the conditions to which the 300 nm long and 1.4 nm diameter monomer building block is exposed.

A space curve describes the path followed by a particle moving through three-dimensional space. Unlike plane curves, which are confined to two coordinates, space curves require three coordinate functions. If t is a parameter, the position of the particle is represented by the vector function\begin{equation*}\mathbf{r}(t)=\langle x(t),y(t),z(t)\rangle,\end{equation*}where x(t), y(t), and z(t) are differentiable functions of t. As t varies over an interval, the endpoints of the position vectors...

A space truss is a three-dimensional counterpart of a planar truss. These structures consist of members connected at their ends, often utilizing ball-and-socket joints to create a stable and versatile framework. The space truss is widely used in various construction projects due to its adaptability and capacity to withstand complex loads. At the core of a space truss lies the fundamental unit known as the tetrahedron. This structure is composed of six members that form a three-dimensional shape...

The frequency-domain technique, commonly used in analyzing and designing feedback control systems, is effective for linear, time-invariant systems. However, it falls short when dealing with nonlinear, time-varying, and multiple-input multiple-output systems. The time-domain or state-space approach addresses these limitations by utilizing state variables to construct simultaneous, first-order differential equations, known as state equations, for an nth-order system. Consider an RLC circuit, a...

Line integrals in space provide a mathematical method for accumulating quantities along a three-dimensional path, such as a thin coiled spring represented by the trajectory curve. The path is defined by a position vector r, which represents the x, y, and z coordinates in terms of a single parameter t, usually time or an angle. As this parameter changes, the vector traces a smooth and continuous curve through space, defining the trajectory.Line Integrals: Scalar-Valued FunctionsFor scalar-valued...