Sierpinski carpet fractal monopole antenna for ultra-wideband applications

Microstrip antenna is broadly used in the modern communication system due to its significant features such as light weight, inexpensive, low profile, and ease of integration with radio frequency devices. The fractal shape is applied in antenna geometry to obtain the ultra-wideband antennas. In this paper, the sierpinski carpet fractal monopole antenna (SCFMA) is developed for base case, first iteration and second iteration to obtain the wideband based on its space filling and self-similar characteristics. The dimension of the monopole patch size is optimized to minimize the overall dimension of the fractal antenna. Moreover, the optimized planar structure is proposed using the microstrip line feed. The monopole antenna is mounted on the FR4 substrate with the thickness of 1.6 mm with loss tangent of 0.02 and relative permittivity of 4.4. The performance of this SCFMA is analyzed in terms of area, bandwidth, return loss, voltage standing wave ratio, radiation pattern and gain. The proposed fractal antenna achieves three different bandwidth ranges such as 2.6-4.0 GHz, 2.5-4.3 GHz and 2.4-4.4 GHz for base case, first and second iteration respectively. The proposed SCFMA is compared with existing fractal antennas to prove the efficiency of the SCFMA design. The area of the SCFMA is 25×20 mm², which is less when compared to the existing fractal antennas.

Molecular Dynamics Investigation on Thermal Conductivity and Photon Behaviors of Graphene With Sierpinski Carpet Fractal Defects

The thermal conductivity (TC) of graphene with Sierpinski carpet fractal (SCF) and regular carpet (RC) defects is numerically studied by the non-equilibrium molecular dynamics (NEMD) method. The influences of porosity, fractal levels, and types of defects on the TC of graphene are clarified, and the underlying mechanisms of phonon behaviors are uncovered. The numerical results indicate that the defects in graphene induce the atoms that have the heat transfer blockage effect, and thus, the TC of defective graphene decreases with increasing porosity. With the increase in fractal levels, more atoms have the heat transfer blockage effect, which induces the TC of graphene with SCF defects to sharply decrease. Moreover, compared with the graphene with RC defects, more atoms participate in the heat transfer blockage under the graphene with SCF defects, which leads to the lower TC of graphene with SCF defects.

New Classes of Regular Symmetric Fractals

The paper introduces new fractal families with annular and checkerboard structures that include the Sierpinski carpet and the Menger sponge as special cases. The complementary mapping is defined and a notation to represent the families is proposed.

Sierpinski Carpet and Chaos in the Periodic Table of the Elements

Fractals are self-similar geometric pattern which can be found in nature. They have applications in mathematic, electronic, architecture. Fractal sets also can be used to create chaotic systems. This work is about applying Sierpinski carpet order on the periodic table of the elements to create a new pattern for the chemical elements. Fibonacci numbers and Math lab software are used to transform a linear system to three spiral systems. This new pattern which is consisted of three layers shows that the flows among chemical elements are based on Archimedes spiral equation The purpose of this study is to show Sierpinski carpet order in the periodic table of the chemical elements and also there can be a chaos even in chemical elements.

Two Classes of Regular Symmetric Fractals

The paper introduces new fractal families with annular and checkerboard structures that include the Sierpinski carpet and the Menger sponge as special cases. The complementary mapping is defined and a notation to represent the families is proposed.

Two Classes of Regular Symmetric Fractals

The paper introduces new fractal families with annular and checkerboard structures that include the Sierpinski carpet and the Menger sponge as special cases. The complementary mapping is defined and a notation to represent the families is proposed.

Utilizing Fractals for Modeling and 3D Printing of Porous Structures

Porous structures exhibiting randomly sized and distributed pores are required in biomedical applications (producing implants), materials science (developing cermet-based materials with desired properties), engineering applications (objects having controlled mass and energy transfer properties), and smart agriculture (devices for soilless cultivation). In most cases, a scaffold-based method is used to design porous structures. This approach fails to produce randomly sized and distributed pores, which is a pressing need as far as the aforementioned application areas are concerned. Thus, more effective porous structure design methods are required. This article presents how to utilize fractal geometry to model porous structures and then print them using 3D printing technology. A mathematical procedure was developed to create stochastic point clouds using the affine maps of a predefined Iterative Function Systems (IFS)-based fractal. In addition, a method is developed to modify a given IFS fractal-generated point cloud. The modification process controls the self-similarity levels of the fractal and ultimately results in a model of porous structure exhibiting randomly sized and distributed pores. The model can be transformed into a 3D Computer-Aided Design (CAD) model using voxel-based modeling or other means for digitization and 3D printing. The efficacy of the proposed method is demonstrated by transforming the Sierpinski Carpet (an IFS-based fractal) into 3D-printed porous structures with randomly sized and distributed pores. Other IFS-based fractals than the Sierpinski Carpet can be used to model and fabricate porous structures effectively. This issue remains open for further research.