Collapse Dynamics of a Homopolymer: Theory and Simulation

We present a scaling theory describing the collapse of a homopolymer chain in poor solvent. At time t after the beginning of the collapse, the original Gaussian chain of length N is streamlined to form N/g segments of length R(t), each containing g ~ t monomers. These segments are statistical quantities representing cylinders of length R ~ t^{1/2} and diameter d ~ t^{1/4}, but structured out of stretched arrays of spherical globules. This prescription incorporates the capillary instability. We compare the time-dependent structure factor derived for our theory with that obtained from ultra-large-scale molecular dynamics simulation with explicit solvent. This is the first time such a detailed comparison of theoretical and simulation predictions of collapsing chain structure has been attempted. The favorable agreement between the theoretical and computed structure factors supports the picture of the coarse-graining process during polymer collapse.Comment: 4 pages, 3 figure

Discrete Morse functions for graph configuration spaces

We present an alternative application of discrete Morse theory for two-particle graph configuration spaces. In contrast to previous constructions, which are based on discrete Morse vector fields, our approach is through Morse functions, which have a nice physical interpretation as two-body potentials constructed from one-body potentials. We also give a brief introduction to discrete Morse theory. Our motivation comes from the problem of quantum statistics for particles on networks, for which generalized versions of anyon statistics can appear.Comment: 26 page

Who is to blame? The relationship between ingroup identification and relative deprivation is moderated by ingroup attributions

Contradictory evidence can be found in the literature about whether ingroup identification and perceived relative deprivation are positively or negatively related. Indeed, theoretical arguments can be made for both effects. It was proposed that the contradictory findings can be explained by considering a hitherto unstudied moderator: The extent to which deprivation is attributed to the ingroup. It was hypothesised that identification would only have a negative impact on deprivation, and that deprivation would only have a negative impact on identification, if ingroup attributions are high. To test this, attributions to the ingroup were experimentally manipulated among British student participants (N = 189) who were asked about their perceived deprivation vis-à-vis German students, yield ing support for the hypotheses

Heavy ozone enrichments from ATMOS infrared solar spectra

Vertical enrichment profiles of stratospheric ^(16)O^(16)O^(18)O and ^(16)O^(18)O^(16)O (hereafter referred to as ^(668)O_3 and ^(686)O_3 respectively) have been derived from space-based solar occultation spectra recorded at 0.01 cm^(−1) resolution by the ATMOS (Atmospheric Trace MOlecule Spectroscopy) Fourier-transform infrared (FTIR) spectrometer. The observations, made during the Spacelab 3 and ATLAS-1, -2, and -3 shuttle missions, cover polar, mid-latitude and tropical regions between 26 to 2.6 mb inclusive (≈ 25 to 41 km). Average enrichments, weighted by molecular ^(48)O_3 density, of (15±6)% were found for ^(668)O_3 and (10±7)% for ^(686)O_3. Defining the mixing ratio of ^(50)O_3 as the sum of those for ^(668)O_3 and ^(686)O_3, an enrichment of (13±5)% was found for ^(50)O_3 (1σ standard deviation). No latitudinal or vertical gradients were found outside this standard deviation. From a series of ground-based measurements by the ATMOS instrument at Table Mountain, California (34.4°N), an average total column ^(668)O_3 enrichment of (17±4)% (1σ standard deviation) was determined, with no significant seasonal variation discernable. Possible biases in the spectral intensities that affect the determination of absolute enrichments are discussed

Ethnic In-Group Favoritism Among Minority and Majority Groups: Testing the Self-Esteem Hypothesis Among Preadolescents

The self-esteem hypothesis in intergroup relations, as proposed by social identity theory (SIT), states that successful intergroup discrimination enhances momentary collective self-esteem. This hypothesis is a source of continuing controversy. Furthermore, although SIT is increasingly used to account for children’s group attitudes, few studies have examined the hypothesis among children. In addition, the hypothesis’s generality makes it important to study among children from different ethnic groups. The present study, conducted among Dutch and Turkish preadolescents, examined momentary collective self-feelings as a consequence of ethnic group evaluations. The results tended to support the self-esteem hypothesis. In-group favoritism was found to have a self-enhancing effect among participants high in ethnic identification. This result was found for ethnic majority (Dutch) and minority (Turkish) participants.

Coupled coarse graining and Markov Chain Monte Carlo for lattice systems

We propose an efficient Markov Chain Monte Carlo method for sampling equilibrium distributions for stochastic lattice models, capable of handling correctly long and short-range particle interactions. The proposed method is a Metropolis-type algorithm with the proposal probability transition matrix based on the coarse-grained approximating measures introduced in a series of works of M. Katsoulakis, A. Majda, D. Vlachos and P. Plechac, L. Rey-Bellet and D.Tsagkarogiannis,. We prove that the proposed algorithm reduces the computational cost due to energy differences and has comparable mixing properties with the classical microscopic Metropolis algorithm, controlled by the level of coarsening and reconstruction procedure. The properties and effectiveness of the algorithm are demonstrated with an exactly solvable example of a one dimensional Ising-type model, comparing efficiency of the single spin-flip Metropolis dynamics and the proposed coupled Metropolis algorithm.Comment: 20 pages, 4 figure

Solving Quantum Ground-State Problems with Nuclear Magnetic Resonance

Quantum ground-state problems are computationally hard problems; for general many-body Hamiltonians, there is no classical or quantum algorithm known to be able to solve them efficiently. Nevertheless, if a trial wavefunction approximating the ground state is available, as often happens for many problems in physics and chemistry, a quantum computer could employ this trial wavefunction to project the ground state by means of the phase estimation algorithm (PEA). We performed an experimental realization of this idea by implementing a variational-wavefunction approach to solve the ground-state problem of the Heisenberg spin model with an NMR quantum simulator. Our iterative phase estimation procedure yields a high accuracy for the eigenenergies (to the 10^-5 decimal digit). The ground-state fidelity was distilled to be more than 80%, and the singlet-to-triplet switching near the critical field is reliably captured. This result shows that quantum simulators can better leverage classical trial wavefunctions than classical computers.Comment: 11 pages, 13 figure