Matching Items (4)

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Wada basins of attraction in diffeomorphic maps

Description

Dividing the plane in half leaves every border point of one region a border point of both regions. Can we divide up the plane into three or more regions such

Dividing the plane in half leaves every border point of one region a border point of both regions. Can we divide up the plane into three or more regions such that any point on the boundary of at least one region is on the border of all the regions? In fact, it is possible to design a dynamical system for which the basins of attractions have this Wada property. In certain circumstances, both the Hénon map, a simple system, and the forced damped pendulum, a physical model, produce Wada basins.

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Created

Date Created
  • 2013-05

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Fractal properties and applications of dendritic filaments in programmable metallization cells

Description

Programmable metallization cell (PMC) technology employs the mechanisms of metal ion transport in solid electrolytes (SE) and electrochemical redox reactions in order to form metallic electrodeposits. When a positive bias

Programmable metallization cell (PMC) technology employs the mechanisms of metal ion transport in solid electrolytes (SE) and electrochemical redox reactions in order to form metallic electrodeposits. When a positive bias is applied to an anode opposite to a cathode, atoms at the anode are oxidized to ions and dissolve into the SE. Under the influence of the electric field, the ions move to the cathode and become reduced to form the electrodeposits. These electrodeposits are filamentary in nature and persistent, and since they are metallic can alter the physical characteristics of the material on which they are formed. PMCs can be used as next generation memories, radio frequency (RF) switches and physical unclonable functions (PUFs).

The morphology of the filaments is impacted by the biasing conditions. Under a relatively high applied electric field, they form as dendritic elements with a low fractal dimension (FD), whereas a low electric field leads to high FD features. Ion depletion effects in the SE due to low ion diffusivity/mobility also influences the morphology by limiting the ion supply into the growing electrodeposit.

Ion transport in SE is due to hopping transitions driven by drift and diffusion force. A physical model of ion hopping with Brownian motion has been proposed, in which the ion transitions are random when time window is larger than characteristic time. The random growth process of filaments in PMC adds entropy to the electrodeposition, which leads to random features in the dendritic patterns. Such patterns has extremely high information capacity due to the fractal nature of the electrodeposits.

In this project, lateral-growth PMCs were fabricated, whose LRS resistance is less than 10Ω, which can be used as RF switches. Also, an array of radial-growth PMCs was fabricated, on which multiple dendrites, all with different shapes, could be grown simultaneously. Those patterns can be used as secure keys in PUFs and authentication can be performed by optical scanning.

A kinetic Monte Carlo (KMC) model is developed to simulate the ion transportation in SE under electric field. The simulation results matched experimental data well that validated the ion hopping model.

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Created

Date Created
  • 2015

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Lateral Ag Electrodeposits in Chalcogenide Glass for Physical Unclonable Function Application

Description

Counterfeiting of goods is a widespread epidemic that is affecting the world economy. The conventional labeling techniques are proving inadequate to thwart determined counterfeiters equipped with sophisticated technologies. There is

Counterfeiting of goods is a widespread epidemic that is affecting the world economy. The conventional labeling techniques are proving inadequate to thwart determined counterfeiters equipped with sophisticated technologies. There is a growing need of a secure labeling that is easy to manufacture and analyze but extremely difficult to copy. Programmable metallization cell technology operates on a principle of controllable reduction of a metal ions to an electrodeposit in a solid electrolyte by application of bias. The nature of metallic electrodeposit is unique for each instance of growth, moreover it has a treelike, bifurcating fractal structure with high information capacity. These qualities of the electrodeposit can be exploited to use it as a physical unclonable function. The secure labels made from the electrodeposits grown in radial structure can provide enhanced authentication and protection from counterfeiting and tampering.

So far only microscale radial structures and electrodeposits have been fabricated which limits their use to labeling only high value items due to high cost associated with their fabrication and analysis. Therefore, there is a need for a simple recipe for fabrication of macroscale structure that does not need sophisticated lithography tools and cleanroom environment. Moreover, the growth kinetics and material characteristics of such macroscale electrodeposits need to be investigated. In this thesis, a recipe for fabrication of centimeter scale radial structure for growing Ag electrodeposits using simple fabrication techniques was proposed. Fractal analysis of an electrodeposit suggested information capacity of 1.27 x 1019. The kinetics of growth were investigated by electrical characterization of the full cell and only solid electrolyte at different temperatures. It was found that mass transport of ions is the rate limiting process in the growth. Materials and optical characterization techniques revealed that the subtle relief like structure and consequently distinct optical response of the electrodeposit provides an added layer of security. Thus, the enormous information capacity, ease of fabrication and simplicity of analysis make macroscale fractal electrodeposits grown in radial programmable metallization cells excellent candidates for application as physical unclonable functions.

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Created

Date Created
  • 2017

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Movement kinematics and fractal properties in Fitts' law task

Description

Fractal analyses examine variability in a time series to look for temporal structure

or pattern that reveals the underlying processes of a complex system. Although fractal

property has been found in many

Fractal analyses examine variability in a time series to look for temporal structure

or pattern that reveals the underlying processes of a complex system. Although fractal

property has been found in many signals in biological systems, how it relates to

behavioral performance and what it implies about the complex system under scrutiny are

still open questions. In this series of experiments, fractal property, movement kinematics,

and behavioral performance were measured on participants performing a reciprocal

tapping task. In Experiment 1, the results indicated that the alpha value from detrended

fluctuation analysis (DFA) reflected deteriorating performance when visual feedback

delay was introduced into the reciprocal tapping task. This finding suggests that this

fractal index is sensitive to performance level in a movement task. In Experiment 2, the

sensitivity of DFA alpha to the coupling strength between sub-processes within a system

was examined by manipulation of task space visibility. The results showed that DFA

alpha was not influenced by disruption of subsystems coupling strength. In Experiment 3,

the sensitivity of DFA alpha to the level of adaptivity in a system under constraints was

examined. Manipulation of the level of adaptivity was not successful, leading to

inconclusive results to this question.

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Created

Date Created
  • 2019