We introduce fractal liquids by generalizing classical liquids of integer dimensions d=1,2,3 to a noninteger dimension dl. The particles composing the liquid are fractal objects and their configuration space is also fractal, with the same dimension. Realizations of our generic model system include microphase separated binary liquids in porous media, and highly branched liquid droplets confined ...

The ventricular-blood interface is geometrically complex due to the presence of ventricular trabeculae carneae (VTC). We introduce a new image-based framework to quantify VTC function using high-resolution computed tomography (CT) imaging and offer new insights into the active role of VTCs during ejection. High-resolution Cine CT scans of a patient with normal cardiac function were acquired at ...

We prove dispersive estimates for the linear Schrödinger evolution associated to an operator −∆+V in R3, where the potential is a signed measure with fractal dimension at least 3/2.

Let λ(X) denote Lebesgue measure. If X ⊆ [0, 1] and r ∈ (0, 1) then the r-Hausdorff capacity of X is denoted by H(X) and is defined to be the infimum of all ∑ ∞ i=0 λ(Ii) r where {Ii}i∈ω is a cover of X by intervals. The r Hausdorff capacity has the same null sets as the r-Hausdorff measure which is familiar from the theory of fractal dimension. It is shown that, given r < 1, it is possible to ...

Purpose – Fractal geometry can be used to model natural objects which cannot be easily represented by the euclidean geometry. However, contemporary computer-aided design (CAD) and computer-aided manufacturing (CAM) systems cannot be used to model a fractal object efficiently. In a general layer manufacturing (LM) workflow, a model described by the euclidean geometry is required in order to gene...

Model-based diagnostic reasoning often leads to a large number of diagnostic hypotheses. The set of diagnoses can be reduced by taking into account extra observations (passive monitoring), measuring additional variables (probing) or executing additional tests (sequential diagnosis/test sequencing). In this paper we combine the above approaches with techniques from Automated Test Pattern Generat...

The fractal interpolation theory was used to the research of road surface roughness, and its simulating method was proposed through the piecewise fractal model. The fractal interpolation model was established for the actual road surface roughness, its influential factors and their laws of influencing were also analyzed, and then the model accuracy was confirmed by the fractal parameters and the...

– The quasienergy spectrum of a Bloch electron affected by dc-ac fields is known to have a fractal structure as function of the so-called electric matching ratio, which is the ratio of the ac field frequency and the Bloch frequency. This paper studies a manifestation of the fractal nature of the spectrum in the system “atom in a standing laser wave”, which is a quantum optical realization of a ...

Das Erstellen von Modellen ist u. a. bei der Entwicklung von Informationssystemen etabliert. Hierbei ist die grafische Repräsentation von Informationsobjekten, d. h. die ein Modell grafisch konstituierenden Zeichen, ein wichtiger Aspekt. Die vorhandene und sich vermehrende Zahl von Modellierungsmethoden und durchaus konkurrierenden Notationen lässt die Erstellung von grundsätzlichen Regeln zur ...

..................................................................................................................................... xiii 1 Einleitung und Motivation ................................................................................................... 1 1.1 Multidisziplinäre Zusammenarbeit ................................................................................ 1 1.2 Hera...