Related papers: A Cook Book of Structure Functions
Roughness determines many functional properties of surfaces, such as adhesion, friction, and (thermal and electrical) contact conductance. Recent analytical models and simulations enable quantitative prediction of these properties from…
In this paper we characterize a function defined on the set of edges of a triangulated surface such that there is a spherical angle structure having the function as the edge invariant (or Delaunay invariant). We also characterize a function…
Electronic structure calculations for solids based on many-electron wavefunctions have been hampered by the argument that for large electron numbers wavefunctions are not a legitimate scientific concept, because they face an exponential…
The extensive use of the structure function (SF) in the field of blazar variability suggests that characteristics time-scales are embedded in the light curves of these objects. We argue that for blazar variability studies, the SF results…
In this paper, we study shape functions depending on closed submanifolds. We prove a new structure theorem that establishes the general structure of the shape derivative for this type of shape function. As a special case we obtain the…
Wavelets, known to be useful in non-linear multi-scale processes and in multi-resolution analysis, are shown to have a q-deformed algebraic structure. The translation and dilation operators of the theory associate with any scaling equation…
Structural balance is a classic property of signed graphs satisfying Heider's seminal axioms. Mathematical sociologists have studied balance theory since its inception in the 1040s. Recent research has focused on the development of dynamic…
A method is described for predicting statistical properties of turbulence. Collections of Fourier amplitudes are represented by nonuniformly spaced modes with enhanced coupling coefficients. The statistics of the full dynamics can be…
We relate the second order structure function of a time series with the power spectrum of the original variable, taking an assumption of statistical stationarity. With this approach, we find that the structure function is strongly…
The great majority of engineered products are subject to thermo-mechanical loads which vary with the product environment during the various phases of its life-cycle (machining, assembly, intended service use...). Those load variations may…
This article discusses the description of wall-bounded turbulence as a deterministic high-dimensional dynamical system of interacting coherent structures, defined as eddies with enough internal dynamics to behave relatively autonomously…
A systematic method is proposed for the determination of the statistical properties of a field consisting of a coherent structure interacting with turbulent linear waves. The explicit expression of the generating functional of the…
The spectral function of density fluctuations, also known as the dynamic structure factor, of a monatomic cubic crystal with vacancies is derived from the macroscopic equations describing transport in crystalline solids. The resonances of…
Variations in distinct restricted spaces of wave functions generate distinct density functionals. In particular, angular momentum projected Slater determinants define a new density functional, compatible simultaneously with angular momentum…
Topology of the spatial coherence function is considered in details. The phase singularity (coherence vortices) structures of coherence function are classified by Hopf index and Brouwer degree in topology. The coherence flux quantization…
This paper presents a set of general strategies for the analysis of structure in amorphous materials and a general approach to assessing the utility of a selected structural description. Measures of structural diversity and utility are…
Our ability to grasp and understand complex phenomena is essentially based on recognizing structures and relating these to each other. For example, any meteorological description of a weather condition and explanation of its evolution…
Several site-testing programs and observatories currently use combined MASS-DIMM instruments for monitoring parameters of optical turbulence. The instrument is described here. After a short recall of the measured quantities and operational…
Seeing-limited resolution in large telescopes working over wide wavelength range depends substantially on the turbulence outer scale and cannot be adequately described by one "seeing" value. We attempt to clarify frequent confusions on this…
Wave steepness is a key geometric variable for describing breaking occurrence and its consequences, including energy dissipation and air entrainment. Using three laboratory campaigns under varying spectral conditions and co-flowing wind…