The porosities of flocs formed from a used drilling mud were determined by measuring sizes and settling speeds of individual flocs. These flocs were produced in a Couette-type flocculator under a variety of combinations of fluid shear and solid concentrations. In the calculation of floc porosities, a floc settling model was employed that can consider the effects of creeping flow through a floc on its settling speed. Results show that floc structure can be well described as a fractal with a fractal dimension of 1.53–1.64 for the floc size range tested. The effects of flocculation conditions, such as fluid shear and solid concentration, on floc porosity and structure were examined. It was found that floc porosity and fractal dimension were not influenced by solid concentration, but they increased as fluid shear decreased. Empirical expressions for the porosity of drilling mud flocs are obtained from both the floc settling model and Stokes’ law. For solid volume fraction in flocs, the relative difference between these two expressions could be as much as 38%. However, the fractal dimensions estimated based on the two settling models are nearly the same.

Small-angle X-ray scattering (SAXS), adsorption and nuclear magnetic resonance (NMR) techniques were used to determine the fractal dimensions (D) of 3 natural reference clays: 1) a kaolinite (KGa-2); 2) a hectorite (SHCa-1), and 3) a Ca-montmorillonite (STx-1). The surfaces of these clays were found to be fractal with D values close to 2.0. This is consistent with the common description of clay mineral surfaces as smooth and planar. Some surface irregularities were observed for hectorite and Ca-montmorillonite as a result of impurities in the materials. The SAXS method generated comparable D values for KGa-2 and STx-1. These results are supported by scanning electron microscopy (SEM). The SAXS and adsorption methods were found to probe the surface irregularities of the clays while the nuclear magnetic resonance (NMR) technique seems to reflect the mass distribution of certain sites in the material. Since the surface nature of clays is responsible for their reactivity in natural systems, SAXS and adsorption techniques would be the methods of choice for their fractal characterization. Due to its wider applicable characterization size-range, the SAXS method appears to be better suited for the determination of the fractal dimensions of clay minerals.

Experimental studies have shown that in small cell neuroendocrine lung carcinomas (SCLC) global opening of the chromatin structure is associated with a higher transcription activity and increase of tumor aggressiveness and metastasis. The study of the fractal characteristics (FD) of nuclear chromatin has been widely used to describe the cell nuclear texture and its changes correspond to changes in nuclear metabolic and transcription activity. Hence, we investigated whether the nuclear fractal dimension could be a prognostic factor in SCLC. Hematoxylin-eosin stained brush cytology slides from 49 patients with SCLC were retrieved from our files. The chromatin (FD) was calculated in digitalized and interactively segmented nuclei using a differential box-counting method. The 3,575 nuclei studied showed a bimodal distribution (peaks at FD1 = 2.115 and FD2 = 2.180). The 75 percentile of the FD was an independent unfavorable prognostic factor for overall survival when tested together with ECOG (Eastern Cooperative Oncology Group) performance status, tumor extension, and therapy in a multivariate Cox regression. Our study corroborates the concept of two main chromatin configurations in small cell neuroendocrine carcinomas and that globally more open chromatin indicates a higher risk of metastasis and therefore a shorter survival of the patient.

We present a single, connected tile which can tile the plane but only nonperiodically. The tile is hexagonal with edge markings, which impose simple rules as to how adjacent tiles are allowed to meet across edges. The first of these rules is a standard matching rule, that certain decorations match across edges. The second condition is a new type of matching rule, which allows tiles to meet only when certain decorations in a particular orientation are given the opposite charge. This forces the tiles to form a hierarchy of triangles, following a central idea of the Socolar–Taylor tilings. However, the new edge-to-edge orientational matching rule forces this structure in a very different way, which allows for a surprisingly simple proof of aperiodicity. We show that the hull of all tilings satisfying our rules is uniquely ergodic and that almost all tilings in the hull belong to a minimal core of tilings generated by substitution. Identifying tilings which are charge-flips of each other, these tilings are shown to have pure point dynamical spectrum and a regular model set structure.

This paper presents the design and development of broadband modified Koch curve microstrip patch antenna with multiband characteristics for spectrum sensing in cognitive radio applications. The proposed spectrum sensing antenna is designed specifically for its efficient operation in the spectrum (1.683–3.05, 4.246–9.714, and 11.25–18 GHz) specified for L, S, C, X, Ku with broadband characteristics and omnidirectional radiation pattern. The validity of the proposed shape is proved by having a comparison with other fractal shapes available in the literature.

The progressions in the field of wireless technology can be highly attributed to the development of antennas, which can access high data rates, provide significant gain and uniform radiation characteristics. One such antenna called the Vivaldi antenna has attracted the utmost attention of the researchers owing to its high gain, wide bandwidth, low cross-polarization, and stable radiation characteristics. Over the years, different procedures have been proposed by several researchers to improve the performance of the Vivaldi antennas. Some of these different approaches are feeding mechanisms, integration of slots, dielectric substrate selection, and radiator shape. Correspondingly, the performance of a Vivaldi antenna can be increased by including dielectric lens, parasitic patch in between two radiators, corrugations, as well as metamaterials. This paper gives a systematic identification, location, and analysis of a large number of performance enhancement methods of Vivaldi antenna design depicting their concepts, advantages, drawbacks, and applications. The principal emphasis of this article is to offer an outline of the developments in the design of Vivaldi antennas over the last few years, where the most important offerings, mostly from IEEE publications, have been emphasized. This review work aims to reveal a promising path to antenna researchers for its advancement using Vivaldi antennas.

In mathematical definition, a fractal is a self-similar subset of Euclidean space whose fractal dimension strictly exceeds its topological dimension which in turn involves a recursive generating methodology that results in contours with infinitely intricate fine structures. Fractal geometry has been used to model complex natural objects such as clouds coastlines, etc., that has space-filling properties. In the past years, several groups of scientists around the globe tried to implement the structure of fractal geometry for applications in the field of electromagnetism, which led to the development of new innovative antenna configurations called “fractal antennas” which is primarily focused in fractal antenna elements, and fractal antenna arrays. It has been demonstrated that by exploiting the recursive nature of fractals, several marvellous kinds of properties can be observed in antennas and arrays. The primary focus of this article is to provide a compressed overview of the developments in fractal-shaped antennas as well as arrays over the last few decades where the most prominent contributions mostly from IEEE journals have been highlighted. The open intention of this review work is to show an encouraging path to antenna researchers for its advancement using fractal geometries.

For Laplacians defined by measures on a bounded domain in ℝn, we prove analogues of the classical eigenvalue estimates for the standard Laplacian: lower bound of sums of eigenvalues by Li and Yau, and gaps of consecutive eigenvalues by Payne, Pólya and Weinberger. This work is motivated by the study of spectral gaps for Laplacians on fractals.

Heating coils utilize the concept of resistive heating to convert electrical energy into thermal energy. Uniform heating of the target area is the key performance indicator for heating coil design. Highly uniform distribution of temperature can be achieved by using a dense metal distribution in the area under consideration, however, this increases the cost of production significantly. A low-cost and efficient heating coil should have excellent temperature uniformity while having minimum metal consumption. In this work, space-filling fractal curves, such as Peano curve, Hilbert curve and Moore curve of various orders, have been studied as geometries for heating coils. In order to compare them in an effective way, the area of the geometries has been held constant at 30 mm × 30 mm and a constant power of 2 W has been maintained across all the geometries. Further, the thickness of the metal coils and their widths have been kept constant for all geometries. Finite Element Analysis (FEA) results show Hilbert and Moore curves of order-4, and Peano curve of order-3 outperform the typical double-spiral heater in terms of temperature uniformity and metal coil length.

A novel multiple-input and multiple-output (MIMO) fractal antenna excited by a coplanar waveguide was investigated in this study. A novel technique was used to improve the isolation of 20 dB between the dual radiating elements by inserting a strip line into the outer edges of the ground plane. A sunflower structure was used to configure the antenna in three steps. At each step, an additional sunflower structure was added with half the size of that used in the previous step to enhance the impedance bandwidth. The measured values of envelop correlation coefficient and total active reflection coefficient indicated that the proposed MIMO antenna has high-diversity performance between radiating elements. Wide dual operating bands of 2–2.9 and 5–10 GHz were obtained, which can support different wireless communications, such as 3G, LTE (2.6 GHz), WLAN (2.4 GHz/5 GHz), WiMAX (2.4 GHz/5GHz), ISM (2.4 GHz/5 GHz), 5G (5–6 GHz), and satellite communications (6–8 GHz). The MIMO fractal antenna with a small size achieved a maximum efficiency of 85% and a peak value gain of 6 dBi, low-channel capacity loss of 0.15–0.4 b/s/Hz, and high isolation between radiating elements is suitable for portable communication devices.

Developing the ability to regulate one's emotions in accordance with contextual demands (i.e., emotion regulation) is a central developmental task of early childhood. These processes are supported by the engagement of the autonomic nervous system (ANS), a physiological hub of a vast network tasked with dynamically integrating real-time experiential inputs with internal motivational and goal states. To date, much of what is known about the ANS and emotion regulation has been based on measures of respiratory sinus arrhythmia, a cardiac indicator of parasympathetic activity. In the present study, we draw from dynamical systems models to introduce two nonlinear indices of cardiac complexity (fractality and sample entropy) as potential indicators of these broader ANS dynamics. Using data from a stratified sample of preschoolers living in high- (i.e., emergency homeless shelter) and low-risk contexts (N = 115), we show that, in conjunction with respiratory sinus arrhythmia, these nonlinear indices may help to clarify important differences in the behavioral manifestations of emotion regulation. In particular, our results suggest that cardiac complexity may be especially useful for discerning active, effortful emotion regulation from less effortful regulation and dysregulation.

Swelling deformation tests of Kunigel bentonite and its sand mixtures were performed in distilled water and NaCl solution. The salinity of NaCl solution has a significant impact on the swelling properties of bentonite, but not on its surface structure. The surface structure was characterized using the fractal dimension Ds. Based on the fractal dimension, a unique curve of the em–pe relationship (em is the void ratio of montmorillonite and pe is the effective stress) at full saturation was introduced to express the swelling deformation of bentonite–sand mixtures. In mixtures with a large bentonite content, the swelling deformation always followed the em–pe relationship. In mixtures with a small bentonite content, when the effective stress reached a threshold, the void ratio of montmorillonite em deviated from the unique em–pe curve due to the appearance of a sand skeleton. The threshold of vertical pressure for mixtures in different solutions and the maximum swelling strains were estimated using the em–pe relationship. The good agreement between estimates and experimental data suggest that the em–pe relationship might be an alternative method for predicting the swelling deformation of bentonite–sand mixtures in salt solution.

A super-wideband microstrip fractal antenna is designed with miniaturized dimensions of 21 mm × 23.5 mm × 1 mm and generation of dual rejection bands for WLAN/WiMAX systems has been achieved. The triangular fractal shape slots are placed inside a circular patch and the antenna is miniaturized by using a repetition frequency resonance technique. The proposed antenna frequency range 2.6–40 GHz operates for VSWR of less than 2. Two band rejections for the frequency ranges 5.1–5.8 GHz and 3.4–3.7 GHz are created by one enhanced slot at the feed line and one split-ring resonator at the back of antenna. HFSS 3D software was used for computer simulation. The proposed antenna is fabricated on the FR4 substrate with 1 mm thickness. The measurement data show good agreement with the simulation results.