Hierarchy of integrable Hamiltonians describing of nonlinear n-wave interaction

In the paper we construct an hierarchy of integrable Hamiltonian systems which describe the variation of n-wave envelopes in nonlinear dielectric medium. The exact solutions for some special Hamiltonians are given in terms of elliptic functions of the first kind.Comment: 17 page

Gravity from self-interaction redux

I correct some recent misunderstandings about, and amplify some details of, an old explicit non-geometrical derivation of GR.Comment: Final, amplified, published version; GRG (2009

Multipole nonlinearity of metamaterials

We report on the linear and nonlinear optical response of metamaterials evoked by first and second order multipoles. The analytical ground on which our approach bases permits for new insights into the functionality of metamaterials. For the sake of clarity we focus here on a key geometry, namely the split-ring resonator, although the introduced formalism can be applied to arbitrary structures. We derive the equations that describe linear and nonlinear light propagation where special emphasis is put on second harmonic generation. This contribution basically aims at stretching versatile and existing concepts to describe light propagation in nonlinear media towards the realm of metamaterials.Comment: 7 pages, 3 figure

Self-degradable Cementitious Sealing Materials

A self-degradable alkali-activated cementitious material consisting of a sodium silicate activator, slag, Class C fly ash, and sodium carboxymethyl cellulose (CMC) additive was formulated as one dry mix component, and we evaluated its potential in laboratory for use as a temporary sealing material for Enhanced Geothermal System (EGS) wells. The self-degradation of alkali-activated cementitious material (AACM) occurred, when AACM heated at temperatures of {ge}200 C came in contact with water. We interpreted the mechanism of this water-initiated self-degradation as resulting from the in-situ exothermic reactions between the reactants yielded from the dissolution of the non-reacted or partially reacted sodium silicate activator and the thermal degradation of the CMC. The magnitude of self-degradation depended on the CMC content; its effective content in promoting degradation was {ge}0.7%. In contrast, no self-degradation was observed from CMC-modified Class G well cement. For 200 C-autoclaved AACMs without CMC, followed by heating at temperatures up to 300 C, they had a compressive strength ranging from 5982 to 4945 psi, which is {approx}3.5-fold higher than that of the commercial Class G well cement; the initial- and final-setting times of this AACM slurry at 85 C were {approx}60 and {approx}90 min. Two well-formed crystalline hydration phases, 1.1 nm tobermorite and calcium silicate hydrate (I), were responsible for developing this excellent high compressive strength. Although CMC is an attractive, as a degradation-promoting additive, its addition to both the AACM and the Class G well cement altered some properties of original cementitious materials; among those were an extending their setting times, an increasing their porosity, and lowering their compressive strength. Nevertheless, a 0.7% CMC-modified AACM as self-degradable cementitious material displayed the following properties before its breakdown by water; {approx}120 min initial- and {approx}180 min final-setting times at 85 C, and 1825 to 1375 psi compressive strength with 51.2 to 55.0% porosity up to 300 C

Stability of central finite difference schemes for the Heston PDE

This paper deals with stability in the numerical solution of the prominent Heston partial differential equation from mathematical finance. We study the well-known central second-order finite difference discretization, which leads to large semi-discrete systems with non-normal matrices A. By employing the logarithmic spectral norm we prove practical, rigorous stability bounds. Our theoretical stability results are illustrated by ample numerical experiments

Functional DNA methylation signatures for autism spectrum disorder genomic risk loci: 16p11.2 deletions and CHD8 variants

Background: Autism spectrum disorder (ASD) is a common and etiologically heterogeneous neurodevelopmental disorder. Although many genetic causes have been identified (\u3e 200 ASD-risk genes), no single gene variant accounts for \u3e 1% of all ASD cases. A role for epigenetic mechanisms in ASD etiology is supported by the fact that many ASD-risk genes function as epigenetic regulators and evidence that epigenetic dysregulation can interrupt normal brain development. Gene-specific DNAm profiles have been shown to assist in the interpretation of variants of unknown significance. Therefore, we investigated the epigenome in patients with ASD or two of the most common genomic variants conferring increased risk for ASD. Genome-wide DNA methylation (DNAm) was assessed using the Illumina Infinium HumanMethylation450 and MethylationEPIC arrays in blood from individuals with ASD of heterogeneous, undefined etiology (n = 52), and individuals with 16p11.2 deletions (16p11.2del, n = 9) or pathogenic variants in the chromatin modifier CHD8 (CHD8 +/-, n = 7). Results: DNAm patterns did not clearly distinguish heterogeneous ASD cases from controls. However, the homogeneous genetically-defined 16p11.2del and CHD8 +/- subgroups each exhibited unique DNAm signatures that distinguished 16p11.2del or CHD8 +/- individuals from each other and from heterogeneous ASD and control groups with high sensitivity and specificity. These signatures also classified additional 16p11.2del (n = 9) and CHD8 (n = 13) variants as pathogenic or benign. Our findings that DNAm alterations in each signature target unique genes in relevant biological pathways including neural development support their functional relevance. Furthermore, genes identified in our CHD8 +/- DNAm signature in blood overlapped differentially expressed genes in CHD8 +/- human-induced pluripotent cell-derived neurons and cerebral organoids from independent studies. Conclusions: DNAm signatures can provide clinical utility complementary to next-generation sequencing in the interpretation of variants of unknown significance. Our study constitutes a novel approach for ASD risk-associated molecular classification that elucidates the vital cross-talk between genetics and epigenetics in the etiology of ASD

Nonlinear optical response and spin-charge separation in one-dimensional Mott insulators

We theoretically study the nonlinear optical response and photoexcited states of the Mott insulators. The nonlinear optical susceptibility \chi^(3) is calculated by using the exact diagonalization technique on small clusters. From the systematic study of the dependence of \chi^(3) on dimensionality, we find that the spin-charge separation plays a crucial role in enhancing \chi^(3) in the one-dimensional (1D) Mott insulators. Based on this result, we propose a holon-doublon model, which describes the nonlinear response in the 1D Mott insulators. These findings show that the spin-charge separation will become a key concept of optoelectronic devices.Comment: 5 pages with 3 figures, to appear in PRB RC, 15 August 200

Intrinsic energy flow in laser-excited 3d ferromagnets

Ultrafast magnetization dynamics are governed by energy flow between electronic, magnetic and lattice degrees of freedom. A quantitative understanding of these dynamics must be based on a model that agrees with experimental results for all three subsystems. However, ultrafast dynamics of the lattice remain largely unexplored experimentally. Here, we combine femtosecond electron diffraction experiments of the lattice dynamics with energy-conserving atomistic spin dynamics (ASD) simulations and ab-initio calculations to study the intrinsic energy flow in the 3d ferromagnets cobalt (Co) and iron (Fe). The simulations yield a good description of experimental data, in particular an excellent description of our experimental results for the lattice dynamics. We find that the lattice dynamics are influenced significantly by the magnetization dynamics due to the energy cost of demagnetization. Our results highlight the role of the spin system as the dominant heat sink in the first hundreds of femtoseconds. Together with previous findings for nickel [1], our work demonstrates that energy-conserving ASD simulations provide a general and consistent description of the laser-induced dynamics in all three elemental 3d ferromagnets