Geometric structure and information change in phase transitions

We propose a toy model for a cyclic order-disorder transition and introduce a new geometric methodology to understand stochastic processes involved in transitions. Specifically, our model consists of a pair of Forward and Backward Processes (FP and BP) for the emergence and disappearance of a structure in a stochastic environment. We calculate time-dependent PDFs and the information length L, which is the total number of different states that a system undergoes during the transition. Time-dependent PDFs during transient relaxation exhibit strikingly different behaviour in FP and BP. In particular, FP driven by instability undergoes the broadening of the PDF with large increase in fluctuations before the transition to the ordered state accompanied by narrowing the PDF width. During this stage, we identify an interesting geodesic solution accompanied by the self-regulation between the growth and nonlinear damping where the time scale τ of information change is constant in time, independent of the strength of the stochastic noise. In comparison, BP is mainly driven by the macroscopic motion due to the movement of the PDF peak. The total information length L between initial and final states is much larger in BP than in FP, increasing linearly with the deviation γ of a control parameter from the critical state in BP while increasing logarithmically with γ in FP. L scales as | ln D| and D‾½ in FP and BP, respectively, where D measures the strength of the stochastic forcing. These differing scalings with γ and D suggest a great utility of L in capturing different underlying processes, specifically, diffusion vs advection in phase transition by geometry. We discuss physical origins of these scalings and comment on implications of our results for bistable systems undergoing repeated order-disorder transitions (e.g. fitness)

Rotational symmetry and degeneracy: a cotangent-perturbed rigid rotator of unperturbed level multiplicity

We predict level degeneracy of the rotational type in diatomic molecules described by means of a cotangent-hindered rigid rotator. The problem is shown to be exactly solvable in terms of non-classical Romanovski polynomials. The energies of such a system are linear combinations of t(t+1) and 1/[t(t+1)+1/4] terms with the non-negative integer principal quantum number t=n+|/bar{m}| being the sum of the degree n of the polynomials and the absolute value, |/bar{m}|, of the square root of the separation constant between the polar and azimuthal motions. The latter obeys, with respect to t, the same branching rule, |/bar{m}|=0,1,..., t, as does the magnetic quantum number with respect to the angular momentum, l, and, in this fashion, the t quantum number presents itself indistinguishable from l. In effect, the spectrum of the hindered rotator has the same (2t+1)-fold level multiplicity as the unperturbed one. For small t values, the wave functions and excitation energies of the perturbed rotator differ from the ordinary spherical harmonics, and the l(l+1) law, respectively, while approaching them asymptotically with increasing t. In this fashion the breaking of the rotational symmetry at the level of the representation functions is opaqued by the level degeneracy. The model provides a tool for the description of rotational bands with anomalously large gaps between the ground state and its first excitation.Comment: 10 pages, 6 figures; Molecular Physics 201

Linkless octree using multi-level perfect hashing

The standard C/C++ implementation of a spatial partitioning data structure, such as octree and quadtree, is often inefficient in terms of storage requirements particularly when the memory overhead for maintaining parent-to-child pointers is significant with respect to the amount of actual data in each tree node. In this work, we present a novel data structure that implements uniform spatial partitioning without storing explicit parent-to-child pointer links. Our linkless tree encodes the storage locations of subdivided nodes using perfect hashing while retaining important properties of uniform spatial partitioning trees, such as coarse-to-fine hierarchical representation, efficient storage usage, and efficient random accessibility. We demonstrate the performance of our linkless trees using image compression and path planning examples.postprin

Cooperative Carbon Dioxide Adsorption in Alcoholamine- and Alkoxyalkylamine-Functionalized Metal-Organic Frameworks.

A series of structurally diverse alcoholamine- and alkoxyalkylamine-functionalized variants of the metal-organic framework Mg2 (dobpdc) are shown to adsorb CO2 selectively via cooperative chain-forming mechanisms. Solid-state NMR spectra and optimized structures obtained from van der Waals-corrected density functional theory calculations indicate that the adsorption profiles can be attributed to the formation of carbamic acid or ammonium carbamate chains that are stabilized by hydrogen bonding interactions within the framework pores. These findings significantly expand the scope of chemical functionalities that can be utilized to design cooperative CO2 adsorbents, providing further means of optimizing these powerful materials for energy-efficient CO2 separations

An International Comparison Study Exploring the Influential Variables Affecting Students’ Reading Literacy and Life Satisfaction

The Program for International Student Assessment (PISA) aims to provide comparative data on 15-year-olds’ academic performance and well-being. The purpose of the current study is to explore and compare the variables that predict the reading literacy and life satisfaction of U.S. and South Korean students. The random forest algorithm, which is a machine learning approach, was applied to PISA 2018 data (4,677 U.S. students and 6,650 South Korean students) to explore and select the key variables among 305 variables that predict reading literacy and life satisfaction. In each random forest analysis, one for the U.S. and another for South Korea, 23 variables were derived as key variables in students’ reading literacy. In addition, 23 variables in the U.S. and 26 variables in South Korea were derived as important variables for students’ life satisfaction. The multilevel analysis revealed that various student-, teacher- or school-related key variables derived from the random forest were statistically related to either U.S. and/or South Korean students’ reading literacy and/or life satisfaction. The current study proposes to use a machine learning approach to examine international large-scale data for an international comparison. The implications of the current study and suggestions for future research are discussed

Finite element analysis for normal pressure hydrocephalus: The effects of the integration of sulci.

Finite element analysis (FEA) is increasingly used to investigate the brain under various pathological changes. Although FEA has been used to study hydrocephalus for decades, previous studies have primarily focused on ventriculomegaly. The present study aimed to investigate the pathologic changes regarding sulcal deformation in normal pressure hydrocephalus (NPH). Two finite element (FE) models-an anatomical brain geometric (ABG) model and the conventional simplified brain geometric (SBG) model-of NPH were constructed. The models were constructed with identical boundary conditions but with different geometries. The ABG model contained details of the sulci geometry, whereas these details were omitted from the SBG model. The resulting pathologic changes were assessed via four biomechanical parameters: pore pressure, von Mises stress, pressure, and void ratio. NPH was induced by increasing the transmantle pressure gradient (TPG) from 0 to a maximum of 2.0 mmHg. Both models successfully simulated the major features of NPH (i.e., ventriculomegaly and periventricular lucency). The changes in the biomechanical parameters with increasing TPG were similar between the models. However, the SBG model underestimated the degree of stress across the cerebral mantle by 150% compared with the ABG model. The SBG model also overestimates the degree of ventriculomegaly (increases of 194.5% and 154.1% at TPG = 2.0 mmHg for the SBG and ABG models, respectively). Including the sulci geometry in a FEA for NPH clearly affects the overall results. The conventional SBG model is inferior to the ABG model, which accurately simulated sulcal deformation and the consequent effects on cortical or subcortical structures. The inclusion of sulci in future FEA for the brain is strongly advised, especially for models used to investigate space-occupying lesions.This research was supported by the Basic Science Research Program through the National Research Foundation of Korea (NRF) funded by the Ministry of Science, ICT & Future Planning (2013R1A1A1004827).This is the author accepted manuscript. The final version is available from Elsevier via http://dx.doi.org/10.1016/j.media.2015.05.00

High Quality Bioreplication of Intricate nanostructures from a Fragile Gecko Skin Surface with Bactericidal Properties

published_or_final_versio