Article
Mathematics, Applied
Yasushi Nagai, Shigeki Akiyama, Jeong-Yup Lee
Summary: This study investigates the existence and non-existence of arithmetic progressions in self-affine tilings, examining how the arithmetic condition of the expansion map affects certain one-dimensional arithmetic progressions, and demonstrating the equivalence of full-rank infinite arithmetic progressions, pure discrete dynamical spectrum, and limit-periodicity in certain self-affine tilings. The research provides a comprehensive overview of the presence or absence of full-rank infinite arithmetic progressions in self-similar tilings.
ERGODIC THEORY AND DYNAMICAL SYSTEMS
(2021)
Article
Computer Science, Theory & Methods
Nikolay Vereshchagin
Summary: We study a family of substitution tilings with similar right triangles of two sizes, obtained using a substitution rule introduced in a previous paper. We provide an alternative proof of the fact that this family of tilings can be obtained from a local rule using decorated tiles. Our approach involves using more decorated tiles but with a more intuitive decoration of supertiles and a simpler local rule.
DISCRETE & COMPUTATIONAL GEOMETRY
(2022)
Article
Mathematics, Applied
Boris Solomyak, Rodrigo Trevino
Summary: This paper extends the construction of a spectral cocycle from the case of one-dimensional substitution flows to the setting of pseudo-self-similar tilings in ${\mathbb R}<^>d$, allowing expanding similarities with rotations. The pointwise upper Lyapunov exponent of this cocycle is used to bound the local dimension of spectral measures of deformed tilings. Following the work of Trevino, the deformations are considered in the simpler, non-random setting, and some of Trevino's results in this special case are reviewed and illustrated on concrete examples.
ERGODIC THEORY AND DYNAMICAL SYSTEMS
(2023)
Article
Engineering, Mechanical
Prasanjit Kumar Kundu, Shyamal Chatterjee
Summary: In this paper, a centralized nonlinear controller is proposed to generate and control self-excited periodic, quasiperiodic, chaotic and hyper-chaotic oscillations in a fully actuated spring-mass-damper mechanical system. The analytical relations among amplitude, frequency and controller parameters have been obtained using the method of two-time scale. Numerical simulations reveal a region of multistability in the plane of control parameters, where system responses can be periodic, quasiperiodic, chaotic or hyper-chaotic depending on initial conditions. The results have potential applications in various macro- and micro-mechanical systems.
NONLINEAR DYNAMICS
(2023)
Article
Computer Science, Artificial Intelligence
Jarkko Kari, Victor H. Lutfalla
Summary: Planar Rosa is a family of rhombus tilings with rotational symmetry that are generated by substitution and are also discrete plane tilings. We prove that Sub Rosa substitution tilings with rotational symmetry do not satisfy the discrete plane condition. This research is important for understanding the characteristics of plane tilings.
Article
Computer Science, Theory & Methods
Jarkko Kari, Victor H. Lutfalla
Summary: This study focuses on substitution tilings that are also discrete plane tilings. We prove that the Sub Rosa substitution tilings with a 2n-fold rotational symmetry are not discrete planes, and then define new Planar Rosa substitution tilings that satisfy the discrete plane condition. Our methods involve using the lift operator to adjust the tilings and substitutions, and applying linear algebra, properties of circulant matrices, and trigonometric sums to study the planarity of substitution tilings in R-n. The construction of the Planar Rosa substitutions also utilizes the Kenyon criterion and a result on De Bruijn multigrid dual tilings.
DISCRETE & COMPUTATIONAL GEOMETRY
(2023)
Article
Mathematics, Applied
Eric Akkermans, Yaroslav Don, Jonathan Rosenberg, Claude L. Schochet
Summary: This paper explores the relationship between the structural aspect of tilings (described by Cech cohomology) and the spectral properties of Hamiltonians defined on those tilings (defined by K-theory), showing their equivalence in dimensions <= 3. A theorem is presented to specify the conditions for this relationship to hold, which can be seen as an extension of the Bloch Theorem to a wide range of aperiodic tilings. The underlying idea behind this result is based on the connection between cohomology and K-theory traces, and their equivalence in low dimensions.
JOURNAL OF GEOMETRY AND PHYSICS
(2021)
Article
Physics, Multidisciplinary
Xiang-Ping Jiang, Yi Qiao, Junpeng Cao
Summary: This study investigates the topological properties of the one-dimensional non-Hermitian Kitaev model with complex either periodic or quasiperiodic potentials. The energy spectrum and phase diagrams of the system are obtained using the transfer matrix method, and the phase transition points are analytically determined. Majorana zero modes are found in the topological nontrivial regimes. Particularly focusing on quasiperiodic potentials, the phase transition from topological superconducting phase to Anderson localization is identified, accompanied by the Anderson localization-delocalization transition in this non-Hermitian system. It is also observed that increasing non-Hermiticity can reduce the topological regime.
Article
Mathematics
Dirk Frettloeh, Yotam Smilansky, Yaar Solomon
Summary: This study focuses on the bounded displacement (BD) equivalence relation on Delone sets and explores instances of non-equivalence. A general condition for two Delone sets to be BD non-equivalent is presented, with applications to tilings of Euclidean space. The results include investigations on substitution tilings and mixed substitution systems generating various BD equivalence classes.
JOURNAL OF COMBINATORIAL THEORY SERIES A
(2021)
Article
Nanoscience & Nanotechnology
Reza Heydarian, Constantin Simovski
Summary: The study investigates the non-resonant mechanism of subwavelength imaging granted by a dielectric microsphere, confirming a hypothesis proposed previously. Numerical simulations demonstrate that the evolution of the phase front of the hollow wave beam formed by the microsphere enables deep subwavelength resolution of two dipole sources. The physical mechanism of imaging is not affected by the use of a 2D sphere in simulations instead of a 3D microsphere.
PHOTONICS AND NANOSTRUCTURES-FUNDAMENTALS AND APPLICATIONS
(2021)
Article
Physics, Mathematical
Rodrigo Trevino
Summary: This paper focuses on globally random substitutions on a finite set of prototiles, using renormalization tools applied to objects from operator algebras to establish upper and lower bounds on the rate of deviations of ergodic averages for the uniquely ergodic Rd action on the tiling spaces obtained from such tilings. These results are applied to statements about the convergence rates for integrated density of states for random Schrodinger operators obtained from aperiodic tilings in the construction.
JOURNAL OF MATHEMATICAL PHYSICS
(2021)
Article
Mathematics
Stanley Alama, Lia Bronsard, Xinyang Lu, Chong Wang
Summary: This study investigates a two-dimensional ternary inhibitory system derived from the sharp-interface limit of the Nakazawa-Ohta density functional theory of triblock copolymers. In this limit, two energy levels are distinguished to encode information on local structures and spatial distribution of components in global minimizers. The main challenge lies in solving a two-component isoperimetric problem, which lacks an explicit formula and exhibits non-concave or non-convex behavior in parts of its domain.
INDIANA UNIVERSITY MATHEMATICS JOURNAL
(2021)
Article
Chemistry, Multidisciplinary
Jeong-Yup Lee
Summary: This paper investigates substitution tilings with pure discrete spectrum and presents their characteristics and properties, comparing them to previous studies.
ACTA CRYSTALLOGRAPHICA A-FOUNDATION AND ADVANCES
(2022)
Article
Automation & Control Systems
Saima Akram, Allah Nawaz, Muhammad Bilal Riaz, Mariam Rehman
Summary: In this article, the maximum possible numbers of periodic solutions for the quartic differential equation are calculated, and new formulae for determining these maximum numbers are developed. Through a systematic procedure of bifurcation analysis and using computer algebra software, the authors successfully obtain a series of results, which are validated and discussed. These new results are a valuable addition to the existing literature.
INTELLIGENT AUTOMATION AND SOFT COMPUTING
(2022)
Article
Computer Science, Information Systems
Supreeti Kamilya, Jarkko Kari
Summary: This study investigates nilpotency in one-dimensional non-uniform cellular automata (NUCA) and finds that changing the distribution of local rules can drastically impact the dynamics of the system. It is proven that in some cases, there may be non-periodic distributions that are not nilpotent even if all periodic distributions are nilpotent. Additionally, the undecidability of determining if a NUCA with a given finite distribution of local rules has a periodic point is established.
Article
Chemistry, Multidisciplinary
Simone Tommasini, Luca Bindi, Maurizio Petrelli, Paul D. Asimow, Paul J. Steinhardt
Summary: This study conducted laser ablation inductively coupled plasma mass spectrometry measurements of trace element contents in two naturally occurring quasicrystalline minerals from the Khatyrka meteorite. The results revealed a unique pattern in the elemental composition, indicating significant differences compared to primitive solar system materials. Additionally, it was found that the natural quasicrystals contain 3-5% silicate and oxide nanopartide inclusions.
ACS EARTH AND SPACE CHEMISTRY
(2021)
Article
Astronomy & Astrophysics
Anna Ijjas, Paul J. Steinhardt
Summary: This paper tracks the evolution of entropy and black holes in a cyclic universe that undergoes repeated intervals of expansion and contraction. The study discovers that after each contraction, entropy naturally reaches near-maximal levels in the matter-radiation sector and near-minimal levels in the gravitational sector.
Article
Multidisciplinary Sciences
Cosmin Andrei, Anna Ijjas, Paul J. Steinhardt
Summary: In this paper, we investigate how short the remaining period of expansion can be given current observational constraints on dark energy, and discuss how this scenario fits naturally with cyclic cosmologies and recent conjectures about quantum gravity.
PROCEEDINGS OF THE NATIONAL ACADEMY OF SCIENCES OF THE UNITED STATES OF AMERICA
(2022)
Article
Physics, Multidisciplinary
Yiqiu Zhao, Yuchen Zhao, Dong Wang, Hu Zheng, Bulbul Chakraborty, Joshua E. S. Socolar
Summary: Dry granular materials can become rigid when compressed or sheared, but their stability properties are not well understood. Experimental observations reveal that under specific conditions, the material can evolve into an "ultrastable" state with nearly elastic stress response.
Article
Physics, Multidisciplinary
Ryan Kozlowski, Hu Zheng, Karen E. Daniels, Joshua E. S. Socolar
Summary: In this study, the effects of grain angularity on stick-slip dynamics in granular materials were experimentally investigated. It was found that packings of triangular or square grains had higher shear strengths and shorter sticking periods compared to packings of pentagons, hexagons, or disks. Additionally, high angularity grains resulted in larger dilation of the medium during sticking periods. These findings suggest that grain angularity plays a significant role in grain-scale flow and macroscopic stick-slip dynamics, with a continuous change in dynamics as the circular grain limit is approached.
FRONTIERS IN PHYSICS
(2022)
Article
Multidisciplinary Sciences
Luca Bindi, Matthew A. Pasek, Chi Ma, Jinping Hu, Guangming Cheng, Nan Yao, Paul D. Asimow, Paul J. Steinhardt
Summary: We report the discovery of a dodecagonal quasicrystal Mn72.3Si15.6Cr9.7Al1.8Ni0.6, composed of a periodic stacking of atomic planes with quasiperiodic translational order and 12-fold symmetry along the two directions perpendicular to the planes, accidentally formed by an electrical discharge event in an eolian dune in Nebraska. The quasicrystal coexists with a cubic crystalline phase and was found in a fulgurite consisting predominantly of fused and melted sand along with traces of melted conductor metal from a downed power line. This discovery suggests the possibility of finding quasicrystals in other places and synthesizing them in the laboratory.
PROCEEDINGS OF THE NATIONAL ACADEMY OF SCIENCES OF THE UNITED STATES OF AMERICA
(2023)
Article
Multidisciplinary Sciences
Michael A. Klatt, Paul J. Steinhardt, Salvatore Torquato
Summary: This study investigates the formation of band gaps in different levels of ordered two-dimensional photonic network solids. The results show that the band gaps rapidly close as the system size increases, except for sufficiently stealthy hyperuniform cases.
PROCEEDINGS OF THE NATIONAL ACADEMY OF SCIENCES OF THE UNITED STATES OF AMERICA
(2022)
Article
Physics, Multidisciplinary
Yiqiu Zhao, Yuchen Zhao, Dong Wang, Hu Zheng, Bulbul Chakraborty, Joshua E. S. Socolar
Summary: In this study, experimental observations of ultrastable states in a shear-jammed granular system subjected to small-amplitude cyclic shear were reported. Further analyses of the data characterized both global and local responses of these ultrastable states within a shear cycle. The results showed a power-law relation between shear modulus and pressure, two types of contacts with different behaviors, and the spatial correlations of the stress tensor were well fitted by a recent theory.
FRONTIERS IN PHYSICS
(2022)
Article
Multidisciplinary Sciences
Qingxia Ma, Hongfei Jiang, Leina Ma, Gaoxiang Zhao, Qianqian Xu, Dong Guo, Ningning He, Hao Liu, Zhaoyuan Meng, Juanjuan Liu, Lei Zhu, Qian Lin, Xiaolin Wu, Min Li, Shudi Luo, Jing Fang, Zhimin Lu
Summary: It has been discovered that the expression levels of the glycolytic enzyme ENO1 are positively correlated with CHKa expression levels in human glioblastoma specimens. ENO1 regulates CHKa expression through post-translational modification. Mechanistically, highly expressed ENO1 in tumor cells binds to I199/F200 of CHKa, leading to the inhibition of TRIM25-mediated poly-ubiquitylation of CHKa at K195 and increased stability of CHKa. These findings provide insight into the integrated regulation of cancer metabolism by the crosstalk between glycolytic and lipidic enzymes.
PROCEEDINGS OF THE NATIONAL ACADEMY OF SCIENCES OF THE UNITED STATES OF AMERICA
(2023)
Article
Geochemistry & Geophysics
Chi Ma, Jinping Hu, Martin D. Suttle, Yunbin Guan, Thomas G. Sharp, Paul D. Asimow, Paul J. Steinhardt, Luca Bindi
Summary: A newly discovered micrometeorite from Sudan exhibits an exotic Al-Cu-Fe assemblage similar to that found in the Khatyrka chondrite. By analyzing oxygen isotope ratios and conducting transmission electron microscopy, researchers found evidence suggesting that the micrometeorite is most likely related to CR chondrites. The study also provides additional evidence for the occurrence of naturally-occurring Al-Cu alloys and suggests the existence of multiple pathways for the association of these two elements.
METEORITICS & PLANETARY SCIENCE
(2023)
Article
Physics, Multidisciplinary
Giorgi Tukhashvili, Paul J. Steinhardt
Summary: We demonstrate that fermion condensation of the Nambu-Jona-Lasinio type can lead to a nonsingular bounce that smoothly connects a phase of slow contraction to a phase of expansion. This approach avoids the problem of generating a large anisotropy and chaotic behavior.
PHYSICAL REVIEW LETTERS
(2023)
Article
Astronomy & Astrophysics
David Garfinkle, Anna Ijjas, Paul J. Steinhardt
Summary: We present the initial findings from a new numerical relativity code that uses a tetrad formulation of the Einstein-scalar field equations and recently introduced gauge/frame invariant diagnostics. The results provide evidence that inflation does not address the issue of homogeneity and isotropy starting from generic initial conditions after the big bang.
Article
Materials Science, Multidisciplinary
Latham Boyle, Paul J. Steinhardt
Summary: This study focuses on 1D quasilattices, particularly self-similar ones, which can be used to generate quasicrystalline tessellations with matching and invertible self-similar substitution rules. The study describes the geometric constructions and equivalence classes of these quasilattices and provides explicit transformation laws between quasilattices in the same class. The study also presents ten special self-similar 1D quasilattices relevant for constructing patterns in higher dimensions and explicitly constructs the corresponding self-same quasilattices.
Article
Materials Science, Multidisciplinary
Latham Boyle, Paul J. Steinhardt
Summary: This study presents a precise geometric relationship between various geometric patterns and expands the number of known examples. By identifying this relationship, the authors are able to systematically obtain these patterns and their properties, and complete the enumeration of quasicrystallographic space groups.
Article
Physics, Fluids & Plasmas
Luis A. Pugnaloni, C. Manuel Carlevaro, Ryan Kozlowski, Hu Zheng, Lou Kondic, Joshua E. S. Socolar
Summary: Experiments and simulations of an intruder dragged by a spring through a two-dimensional annulus of granular material show robust force fluctuations. A simple model predicts the relationship between the critical packing fraction and the width and diameter of the annulus, allowing for a data collapse. These findings challenge theories of mechanical failure in amorphous materials.
