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Ge1-ySny alloys represent a new class of photonic materials for integrated optoelectronics on Si. In this work, the electrical and optical properties of Ge1-ySny alloy films grown on Si, with concentrations in the range 0 ≤ y ≤ 0.04, are studied via a variety of methods. The first microelectronic devices

Ge1-ySny alloys represent a new class of photonic materials for integrated optoelectronics on Si. In this work, the electrical and optical properties of Ge1-ySny alloy films grown on Si, with concentrations in the range 0 ≤ y ≤ 0.04, are studied via a variety of methods. The first microelectronic devices from GeSn films were fabricated using newly developed CMOS-compatible protocols, and the devices were characterized with respect to their electrical properties and optical response. The detectors were found to have a detection range that extends into the near-IR, and the detection edge is found to shift to longer wavelengths with increasing Sn content, mainly due to the compositional dependence of the direct band gap E0. With only 2 % Sn, all of the telecommunication bands are covered by a single detector. Room temperature photoluminescence was observed from GeSn films with Sn content up to 4 %. The peak wavelength of the emission was found to shift to lower energies with increasing Sn content, corresponding to the decrease in the direct band gap E0 of the material. An additional peak in the spectrum was assigned to the indirect band gap. The separation between the direct and indirect peaks was found to decrease with increasing Sn concentration, as expected. Electroluminescence was also observed from Ge/Si and Ge0.98Sn0.02 photodiodes under forward bias, and the luminescence spectra were found to match well with the observed photoluminescence spectra. A theoretical expression was developed for the luminescence due to the direct band gap and fit to the data.
ContributorsMathews, Jay (Author) / Menéndez, Jose (Thesis advisor) / Kouvetakis, John (Thesis advisor) / Drucker, Jeffery (Committee member) / Chizmeshya, Andrew (Committee member) / Ponce, Fernando (Committee member) / Arizona State University (Publisher)
Created2011
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This thesis describes the fabrication of several new classes of Ge1-x-ySixSny materials with the required compositions and crystal quality to engineer the band gaps above and below that of elemental Ge (0.8 eV) in the near IR. The work initially focused on Ge1-x-ySixSny (1-5% Sn, 4-20% Si) materials grown on

This thesis describes the fabrication of several new classes of Ge1-x-ySixSny materials with the required compositions and crystal quality to engineer the band gaps above and below that of elemental Ge (0.8 eV) in the near IR. The work initially focused on Ge1-x-ySixSny (1-5% Sn, 4-20% Si) materials grown on Ge(100) via gas-source epitaxy of Ge4H10, Si4H10 and SnD4. Both intrinsic and doped layers were produced with defect-free microstructure and viable thickness, allowing the fabrication of high-performance photodetectors. These exhibited low ideality factors, state-of-the-art dark current densities and adjustable absorption edges between 0.87 and 1.03 eV, indicating that the band gaps span a significant range above that of Ge. Next Sn-rich Ge1-x-ySixSny alloys (2-4% Si and 4-10% Sn) were fabricated directly on Si and were found to show significant optical emission using photoluminescence measurements, indicating that the alloys have direct band gaps below that of pure Ge in the range of 0.7-0.55 eV. A series of Sn-rich Ge1-x-ySixSny analogues (y>x) with fixed 3-4% Si content and progressively increasing Sn content in the 4-10% range were then grown on Ge buffered Si platforms for the purpose of improving the material's crystal quality. The films in this case exhibited lower defect densities than those grown on Si, allowing a meaningful study of both the direct and indirect gaps. The results show that the separation of the direct and indirect edges can be made smaller than in Ge even for non-negligible 3-4% Si content, confirming that with a suitable choice of Sn compositions the ternary Ge1-x-ySixSny reproduces all features of the electronic structure of binary Ge1-ySny, including the sought-after indirect-to-direct gap cross over. The above synthesis of optical quality Ge1-x-ySixSny on virtual Ge was made possible by the development of high quality Ge-on-Si buffers via chemical vapor deposition of Ge4H10. The resultant films exhibited structural and electrical properties significantly improved relative to state-of-the-art results obtained using conventional approaches. It was found that pure Ge4H10 facilitates the control of residual doping and enables p-i-n devices whose dark currents are not entirely determined by defects and whose zero-bias collection efficiencies are higher than those obtained from samples fabricated using alternative Ge-on-Si approaches.
ContributorsXu, Chi (Author) / Kouvetakis, John (Thesis advisor) / Menéndez, Jose (Thesis advisor) / Chizmeshya, Andrew (Committee member) / Drucker, Jeffrey (Committee member) / Ponce, Fernando (Committee member) / Arizona State University (Publisher)
Created2013
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Description
The thesis studies new methods to fabricate optoelectronic Ge1-ySny/Si(100) alloys and investigate their photoluminescence (PL) properties for possible applications in Si-based photonics including IR lasers. The work initially investigated the origin of the difference between the PL spectrum of bulk Ge, dominated by indirect gap emission, and the PL spectrum

The thesis studies new methods to fabricate optoelectronic Ge1-ySny/Si(100) alloys and investigate their photoluminescence (PL) properties for possible applications in Si-based photonics including IR lasers. The work initially investigated the origin of the difference between the PL spectrum of bulk Ge, dominated by indirect gap emission, and the PL spectrum of Ge-on-Si films, dominated by direct gap emission. It was found that the difference is due to the supression of self-absorption effects in Ge films, combined with a deviation from quasi-equilibrium conditions in the conduction band of undoped films. The latter is confirmed by a model suggesting that the deviation is caused by the shorter recombination lifetime in the films relative to bulk Ge. The knowledge acquired from this work was then utilized to study the PL properties of n-type Ge1-ySny/Si (y=0.004-0.04) samples grown via chemical vapor deposition of Ge2H6/SnD4/P(GeH3)3. It was found that the emission intensity (I) of these samples is at least 10x stronger than observed in un-doped counterparts and that the Idir/Iind ratio of direct over indirect gap emission increases for high-Sn contents due to the reduced gamma-L valley separation, as expected. Next the PL investigation was expanded to samples with y=0.05-0.09 grown via a new method using the more reactive Ge3H8 in place of Ge2H6. Optical quality, 1-um thick Ge1-ySny/Si(100) layers were produced using Ge3H10/SnD4 and found to exhibit strong, tunable PL near the threshold of the direct-indirect bandgap crossover. A byproduct of this study was the development of an enhanced process to produce Ge3H8, Ge4H10, and Ge5H12 analogs for application in ultra-low temperature deposition of Group-IV semiconductors. The thesis also studies synthesis routes of an entirely new class of semiconductor compounds and alloys described by Si5-2y(III-V)y (III=Al, V= As, P) comprising of specifically designed diamond-like structures based on a Si parent lattice incorporating isolated III-V units. The common theme of the two thesis topics is the development of new mono-crystalline materials on ubiquitous silicon platforms with the objective of enhancing the optoelectronic performance of Si and Ge semiconductors, potentially leading to the design of next generation optical devices including lasers, detectors and solar cells.
ContributorsGrzybowski, Gordon (Author) / Kouvetakis, John (Thesis advisor) / Chizmeshya, Andrew (Committee member) / Menéndez, Jose (Committee member) / Arizona State University (Publisher)
Created2013
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Description
One dimensional (1D) and quasi-one dimensional quantum wires have been a subject of both theoretical and experimental interest since 1990s and before. Phenomena such as the "0.7 structure" in the conductance leave many open questions. In this dissertation, I study the properties and the internal electron states of semiconductor quantum

One dimensional (1D) and quasi-one dimensional quantum wires have been a subject of both theoretical and experimental interest since 1990s and before. Phenomena such as the "0.7 structure" in the conductance leave many open questions. In this dissertation, I study the properties and the internal electron states of semiconductor quantum wires with the path integral Monte Carlo (PIMC) method. PIMC is a tool for simulating many-body quantum systems at finite temperature. Its ability to calculate thermodynamic properties and various correlation functions makes it an ideal tool in bridging experiments with theories. A general study of the features interpreted by the Luttinger liquid theory and observed in experiments is first presented, showing the need for new PIMC calculations in this field. I calculate the DC conductance at finite temperature for both noninteracting and interacting electrons. The quantized conductance is identified in PIMC simulations without making the same approximation in the Luttinger model. The low electron density regime is subject to strong interactions, since the kinetic energy decreases faster than the Coulomb interaction at low density. An electron state called the Wigner crystal has been proposed in this regime for quasi-1D wires. By using PIMC, I observe the zig-zag structure of the Wigner crystal. The quantum fluctuations suppress the long range correla- tions, making the order short-ranged. Spin correlations are calculated and used to evaluate the spin coupling strength in a zig-zag state. I also find that as the density increases, electrons undergo a structural phase transition to a dimer state, in which two electrons of opposite spins are coupled across the two rows of the zig-zag. A phase diagram is sketched for a range of densities and transverse confinements. The quantum point contact (QPC) is a typical realization of quantum wires. I study the QPC by explicitly simulating a system of electrons in and around a Timp potential (Timp, 1992). Localization of a single electron in the middle of the channel is observed at 5 K, as the split gate voltage increases. The DC conductance is calculated, which shows the effect of the Coulomb interaction. At 1 K and low electron density, a state similar to the Wigner crystal is found inside the channel.
ContributorsLiu, Jianheng, 1982- (Author) / Shumway, John B (Thesis advisor) / Schmidt, Kevin E (Committee member) / Chen, Tingyong (Committee member) / Yu, Hongbin (Committee member) / Ros, Robert (Committee member) / Arizona State University (Publisher)
Created2012
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Description
Nitride semiconductors have wide applications in electronics and optoelectronics technologies. Understanding the nature of the optical recombination process and its effects on luminescence efficiency is important for the development of novel devices. This dissertation deals with the optical properties of nitride semiconductors, including GaN epitaxial layers and more complex heterostructures.

Nitride semiconductors have wide applications in electronics and optoelectronics technologies. Understanding the nature of the optical recombination process and its effects on luminescence efficiency is important for the development of novel devices. This dissertation deals with the optical properties of nitride semiconductors, including GaN epitaxial layers and more complex heterostructures. The emission characteristics are examined by cathodoluminescence spectroscopy and imaging, and are correlated with the structural and electrical properties studied by transmission electron microscopy and electron holography. Four major areas are covered in this dissertation, which are described next. The effect of strain on the emission characteristics in wurtzite GaN has been studied. The values of the residual strain in GaN epilayers with different dislocation densities are determined by x-ray diffraction, and the relationship between exciton emission energy and the in-plane residual strain is demonstrated. It shows that the emission energy increases withthe magnitude of the in-plane compressive strain. The temperature dependence of the emission characteristics in cubic GaN has been studied. It is observed that the exciton emission and donor-acceptor pair recombination behave differently with temperature. The donor-bound exciton binding energy has been measured to be 13 meV from the temperature dependence of the emission spectrum. It is also found that the ionization energies for both acceptors and donors are smaller in cubic compared with hexagonal structures, which should contribute to higher doping efficiencies. A comprehensive study on the structural and optical properties is presented for InGaN/GaN quantum wells emitting in the blue, green, and yellow regions of the electromagnetic spectrum. Transmission electron microscopy images indicate the presence of indium inhomogeneties which should be responsible for carrier localization. The temperature dependence of emission luminescence shows that the carrier localization effects become more significant with increasing emission wavelength. On the other hand, the effect of non-radiative recombination on luminescence efficiency also varies with the emission wavelength. The fast increase of the non-radiative recombination rate with temperature in the green emitting QWs contributes to the lower efficiency compared with the blue emitting QWs. The possible saturation of non-radiative recombination above 100 K may explain the unexpected high emission efficiency for the yellow emitting QWs Finally, the effects of InGaN underlayers on the electronic and optical properties of InGaN/GaN quantum wells emitting in visible spectral regions have been studied. A significant improvement of the emission efficiency is observed, which is associated with a blue shift in the emission energy, a reduced recombination lifetime, an increased spatial homogeneity in the luminescence, and a weaker internal field across the quantum wells. These are explained by a partial strain relaxation introduced by the InGaN underlayer, which is measured by reciprocal space mapping of the x-ray diffraction intensity.
ContributorsLi, Di (Author) / Ponce, Fernando (Thesis advisor) / Culbertson, Robert (Committee member) / Yu, Hongbin (Committee member) / Shumway, John (Committee member) / Menéndez, Jose (Committee member) / Arizona State University (Publisher)
Created2012
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Description
This dissertation is on the study of structural and optical properties of some III-V and II-VI compound semiconductors. The first part of this dissertation is a study of the deformation mechanisms associated with nanoindentation and nanoscratching of InP, GaN, and ZnO crystals. The second part is an investigation of some

This dissertation is on the study of structural and optical properties of some III-V and II-VI compound semiconductors. The first part of this dissertation is a study of the deformation mechanisms associated with nanoindentation and nanoscratching of InP, GaN, and ZnO crystals. The second part is an investigation of some fundamental issues regarding compositional fluctuations and microstructure in GaInNAs and InAlN alloys. In the first part, the microstructure of (001) InP scratched in an atomic force microscope with a small diamond tip has been studied as a function of applied normal force and crystalline direction in order to understand at the nanometer scale the deformation mechanisms in the zinc-blende structure. TEM images show deeper dislocation propagation for scratches along <110> compared to <100>. High strain fields were observed in <100> scratches, indicating hardening due to locking of dislocations gliding on different slip planes. Reverse plastic flow have been observed in <110> scratches in the form of pop-up events that result from recovery of stored elastic strain. In a separate study, nanoindentation-induced plastic deformation has been studied in c-, a-, and m-plane ZnO single crystals and c-plane GaN respectively, to study the deformation mechanism in wurtzite hexagonal structures. TEM results reveal that the prime deformation mechanism is slip on basal planes and in some cases, on pyramidal planes, and strain built up along particular directions. No evidence of phase transformation or cracking was observed in both materials. CL imaging reveals quenching of near band-edge emission by dislocations. In the second part, compositional inhomogeneity in quaternary GaInNAs and ternary InAlN alloys has been studied using TEM. It is shown that exposure to antimony during growth of GaInNAs results in uniform chemical composition in the epilayer, as antimony suppresses the surface mobility of adatoms that otherwise leads to two-dimensional growth and elemental segregation. In a separate study, compositional instability is observed in lattice-matched InAlN films grown on GaN, for growth beyond a certain thickness. Beyond 200 nm of thickness, two sub-layers with different indium content are observed, the top one with lower indium content.
ContributorsHuang, Jingyi (Author) / Ponce, Fernando A. (Thesis advisor) / Carpenter, Ray W (Committee member) / Smith, David J. (Committee member) / Yu, Hongbin (Committee member) / Treacy, Michael Mj (Committee member) / Arizona State University (Publisher)
Created2013
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Description
Group IV alloy films exhibit the ability to tune both band structure and lattice parameters and have recently attracted attention for their potential applications in Si-photonics and photovoltaics. In this work, several new approaches to produce these alloys directly on Si(100) and Ge(100) wafers are developed. For photovoltaics, use of

Group IV alloy films exhibit the ability to tune both band structure and lattice parameters and have recently attracted attention for their potential applications in Si-photonics and photovoltaics. In this work, several new approaches to produce these alloys directly on Si(100) and Ge(100) wafers are developed. For photovoltaics, use of Ge-buffered Si(100) wafers as a low cost platform for epitaxy of In1-xGaxAs layers was explored. The results indicate that this approach has promise for transitioning from bulk Ge platforms to virtual substrates for a significant cost reduction. The electrical and optical properties of Ge and Ge1-ySny layers produced using several different techniques were explored via fabrication of high performance heterostructure photodiodes. First, a new CVD approach to Ge-like materials was developed in which germanium is alloyed with very small amounts of tin. These alloys exhibited no significant difference in their structural properties or band gap compared to pure Ge, however superior photo response and reduced dark currents were observed from fabricated devices relative to pure Ge on Si reference diodes. Additionally, pure Ge/Si(100) photodiodes were fabricated using layers grown via reactions of Ge4H10 on Si(100) and found to exhibit low dark current densities with high collection efficiencies. Ge1-x-ySixSny materials represent the newest member of group IV alloy family. The ability to decouple the lattice constant and the band gap in this system has led to strong interest both for strain/confinement layers in quantum well structures, and as the possible "missing" 1 eV junction in multijunction photovoltaics. Recent progress in this field has allowed for the first time growth, fabrication and measurement of novel photodiodes based on Ge1-x-ySixSny. This work presents the material, electrical and optical properties of Ge1-x-ySixSny layers and photodiodes grown directly on Ge and Si wafers using two different synthetic approaches. A series of photodiodes containing Sn concentrations from 1-5%, all lattice matched to Ge, was fabricated. The devices exhibited low dark current densities with high collection efficiencies as required for photovoltaics. By measuring the photoresponse, tunable band gaps ranging from 0.85 eV to 1.02 eV were observed.
ContributorsBeeler, Richard (Author) / Kouvetakis, John (Thesis advisor) / Menéndez, Jose (Committee member) / Chizmeshya, Andrew (Committee member) / Arizona State University (Publisher)
Created2012
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Description
Studying charge transport through single molecules tethered between two metal electrodes is of fundamental importance in molecular electronics. Over the years, a variety of methods have been developed in attempts of performing such measurements. However, the limitation of these techniques is still one of the factors that prohibit one from

Studying charge transport through single molecules tethered between two metal electrodes is of fundamental importance in molecular electronics. Over the years, a variety of methods have been developed in attempts of performing such measurements. However, the limitation of these techniques is still one of the factors that prohibit one from gaining a thorough understanding of single molecule junctions. Firstly, the time resolution of experiments is typically limited to milli to microseconds, while molecular dynamics simulations are carried out on the time scale of pico to nanoseconds. A huge gap therefore persists between the theory and the experiments. This thesis demonstrates a nanosecond scale measurement of the gold atomic contact breakdown process. A combined setup of DC and AC circuits is employed, where the AC circuit reveals interesting observations in nanosecond scale not previously seen using conventional DC circuits. The breakdown time of gold atomic contacts is determined to be faster than 0.1 ns and subtle atomic events are observed within nanoseconds. Furthermore, a new method based on the scanning tunneling microscope break junction (STM-BJ) technique is developed to rapidly record thousands of I-V curves from repeatedly formed single molecule junctions. 2-dimensional I-V and conductance-voltage (G-V) histograms constructed using the acquired data allow for more meaningful statistical analysis to single molecule I-V characteristics. The bias voltage adds an additional dimension to the conventional single molecule conductance measurement. This method also allows one to perform transition voltage spectra (TVS) for individual junctions and to study the correlation between the conductance and the tunneling barrier height. The variation of measured conductance values is found to be primarily determined by the poorly defined contact geometry between the molecule and metal electrodes, rather than the tunnel barrier height. In addition, the rapid I-V technique is also found useful in studying thermoelectric effect in single molecule junctions. When applying a temperature gradient between the STM tip and substrate in air, the offset current at zero bias in the I-V characteristics is a measure of thermoelectric current. The rapid I-V technique allows for statistical analysis of such offset current at different temperature gradients and thus the Seebeck coefficient of single molecule junctions is measured. Combining with single molecule TVS, the Seebeck coefficient is also found to be a measure of tunnel barrier height.
ContributorsGuo, Shaoyin (Author) / Tao, Nongjian (Thesis advisor) / Bennett, Peter (Committee member) / Ning, Cun-Zheng (Committee member) / Yu, Hongbin (Committee member) / Arizona State University (Publisher)
Created2012
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Recently a new materials platform consisting of semiconductors grown on GaSb and InAs substrates with lattice constants close to 6.1 A was proposed by our group for various electronic and optoelectronic applications. This materials platform consists of both II-VI (MgZnCdHg)(SeTe) and III-V (InGaAl)(AsSb) compound semiconductors, which have direct bandgaps spanning

Recently a new materials platform consisting of semiconductors grown on GaSb and InAs substrates with lattice constants close to 6.1 A was proposed by our group for various electronic and optoelectronic applications. This materials platform consists of both II-VI (MgZnCdHg)(SeTe) and III-V (InGaAl)(AsSb) compound semiconductors, which have direct bandgaps spanning the entire energy spectrum from far-IR (~0 eV) up to UV (~3.4 eV). The broad range of bandgaps and material properties make it very attractive for a wide range of applications in optoelectronics, such as solar cells, laser diodes, light emitting diodes, and photodetectors. Moreover, this novel materials system potentially offers unlimited degrees of freedom for integration of electronic and optoelectronic devices onto a single substrate while keeping the best possible materials quality with very low densities of misfit dislocations. This capability is not achievable with any other known lattice-matched semiconductors on any available substrate. In the 6.1-A materials system, the semiconductors ZnTe and GaSb are almost perfectly lattice-matched with a lattice mismatch of only 0.13%. Correspondingly, it is expected that high quality ZnTe/GaSb and GaSb/ZnTe heterostructures can be achieved with very few dislocations generated during growth. To fulfill the task, their MBE growth and material properties are carefully investigated. High quality ZnTe layers grown on various III-V substrates and GaSb grown on ZnTe are successfully achieved using MBE. It is also noticed that ZnTe and GaSb have a type-I band-edge alignment with large band offsets (delta_Ec=0.934 eV, delta_Ev=0.6 eV), which provides strong confinement for both electrons and holes. Furthermore, a large difference in refractive index is found between ZnTe and GaSb (2.7 and 3.9, respectively, at 0.7 eV), leading to excellent optical confinement of the guided optical modes in planar semiconductor lasers or distributed Bragg reflectors (DBR) for vertical-cavity surface-emitting lasers. Therefore, GaSb/ZnTe double-heterostructure and ZnTe/GaSb DBR structure are suitable for use in light emitting devices. In this thesis work, experimental demonstration of these structures with excellent structural and optical properties is reported. During the exploration on the properties of various ZnTe heterostructures, it is found that residual tensile strains exist in the thick ZnTe epilayers when they are grown on GaAs, InP, InAs and GaSb substrates. The presence of tensile strains is due to the difference in thermal expansion coefficients between the epilayers and the substrates. The defect densities in these ZnTe layers become lower as the ZnTe layer thickness increases. Growth of high quality GaSb on ZnTe can be achieved using a temperature ramp during growth. The influence of temperature ramps with different ramping rates in the optical properties of GaSb layer is studied, and the samples grown with a temperature ramp from 360 to 470 C at a rate of 33 C/min show the narrowest bound exciton emission peak with a full width at half maximum of 15 meV. ZnTe/GaSb DBR structures show excellent reflectivity properties in the mid-infrared range. A peak reflectance of 99% with a wide stopband of 480 nm centered at 2.5 um is measured from a ZnTe/GaSb DBR sample of only 7 quarter-wavelength pairs.
ContributorsFan, Jin (Author) / Zhang, Yong-Hang (Thesis advisor) / Smith, David (Committee member) / Yu, Hongbin (Committee member) / Menéndez, Jose (Committee member) / Johnson, Shane (Committee member) / Arizona State University (Publisher)
Created2012
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Description
What can classical chaos do to quantum systems is a fundamental issue highly relevant to a number of branches in physics. The field of quantum chaos has been active for three decades, where the focus was on non-relativistic quantumsystems described by the Schr¨odinger equation. By developing an efficient method to

What can classical chaos do to quantum systems is a fundamental issue highly relevant to a number of branches in physics. The field of quantum chaos has been active for three decades, where the focus was on non-relativistic quantumsystems described by the Schr¨odinger equation. By developing an efficient method to solve the Dirac equation in the setting where relativistic particles can tunnel between two symmetric cavities through a potential barrier, chaotic cavities are found to suppress the spread in the tunneling rate. Tunneling rate for any given energy assumes a wide range that increases with the energy for integrable classical dynamics. However, for chaotic underlying dynamics, the spread is greatly reduced. A remarkable feature, which is a consequence of Klein tunneling, arise only in relativistc quantum systems that substantial tunneling exists even for particle energy approaching zero. Similar results are found in graphene tunneling devices, implying high relevance of relativistic quantum chaos to the development of such devices. Wave propagation through random media occurs in many physical systems, where interesting phenomena such as branched, fracal-like wave patterns can arise. The generic origin of these wave structures is currently a matter of active debate. It is of fundamental interest to develop a minimal, paradigmaticmodel that can generate robust branched wave structures. In so doing, a general observation in all situations where branched structures emerge is non-Gaussian statistics of wave intensity with an algebraic tail in the probability density function. Thus, a universal algebraic wave-intensity distribution becomes the criterion for the validity of any minimal model of branched wave patterns. Coexistence of competing species in spatially extended ecosystems is key to biodiversity in nature. Understanding the dynamical mechanisms of coexistence is a fundamental problem of continuous interest not only in evolutionary biology but also in nonlinear science. A continuous model is proposed for cyclically competing species and the effect of the interplay between the interaction range and mobility on coexistence is investigated. A transition from coexistence to extinction is uncovered with a non-monotonic behavior in the coexistence probability and switches between spiral and plane-wave patterns arise. Strong mobility can either promote or hamper coexistence, while absent in lattice-based models, can be explained in terms of nonlinear partial differential equations.
ContributorsNi, Xuan (Author) / Lai, Ying-Cheng (Thesis advisor) / Huang, Liang (Committee member) / Yu, Hongbin (Committee member) / Akis, Richard (Committee member) / Arizona State University (Publisher)
Created2012