As the Internet becomes severely overburdened with exponentially growing traffic demand, it becomes a general belief that a new generation data network is in urgent need today. However, standing at this crossroad, we find that we are in a situation that lacks a theory of network designing. This issue becomes even more serious as the recent progress of network measurement and modeling challenges...

A new method for the design of waverider con-gurations with generalized shock geometries is presented. An arbitrary three-dimensional shock shape is speciied as input, and a cross-stream Euler marching procedure is used to deene the post-shock ow-eld. Unlike most previous studies, this approach allows for the use of nonaxisymmetric shock topologies with nonconstant shock strengths. The problem'...

Dirac stated that the Cartesian coordinates are uniquely suited for expressing canonical commutation relations in a simple form. By contrast, these any other coordinate system is more complicated and less obvious. The question we address this work reason why true. We claim unique role of result existence uniqueness Hofer metric on space transformations phase getting quantized.

Complex and interesting electromagnetic behavior can be found in spaces with non-flat topology. When considering the properties of an electromagnetic medium under an arbitrary coordinate transformation an alternative interpretation presents itself. The transformed material property tensors may be interpreted as a different set of material properties in a flat, Cartesian space. We describe the c...

The present study introduces a new approach to determining optimal electrode positions in transcranial direct current stimulation (tDCS). Electric field and 3D conduction current density were analyzed using 3D finite element method (FEM) formulated for a dc conduction problem. The electrode positions for minimal current injection were optimized by changing the Cartesian coordinate system into t...

We introduce suitable coordinate systems for interacting many-body systems with invariant manifolds. These are Cartesian in coordinate and momentum space and chosen such that several components are identically zero for motion on the invariant manifold. In this sense these coordinates are collective. We make a connection to Zickendraht’s collective coordinates and present certain configurations ...

HUMAN NAVIGATION IS SPECIAL: we use geographic maps to capture a world far beyond our unaided locomotion. In consequence, human navigation is widely thought to depend on internalized versions of these maps - enduring, geocentric 'cognitive maps' capturing diverse information about the environment. Contrary to this view, we argue that human navigation is best studied in relation to research on n...

We introduce a new method to accurately "project" a Cartesian force field onto an internal coordinate molecular model with fixed-bond geometry. The algorithm automatically generates the Internal Coordinate Force Field (ICFF), which is a close approximation of the "source" Cartesian force field. The ICFF method reduces the number of free variables in a model by at least 10-fold and facilitates t...

Abstract. Rigorous equations in compact symbolic matrix notation are introduced to transform coordinates and velocities between ITRF frames and modern GPS-based geocentric geodetic datums. The theory is general but after neglecting higher than second-order terms it is shown that the equations revert to the formulation currently applied in most major continental datums. We discuss several exampl...

A widespread, intuitive and computationally inexpensive method to analyze light guidance through waveguide bends is by introducing an equivalent straight waveguide with refractive index profile modified to account for actual waveguide bend. Here we revise the commonly used equivalent-index formula, ending up with its simple extension that enables rigorous treatment of oneand two-dimensionally c...