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Simulational studies of spin glasses since the early 2010s have focused on the so-called replicon exponent α as a means of determining whether the low-temperature phase of spin glasses is described by the replica symmetry breaking picture of Parisi or by the droplet-scaling picture. On the latter picture, it should be zero, but we shall argue that it will only be zero for systems of linear dimension L>L^*. The crossover length L^* may be of the order of hundreds of lattice spacings in three dimensions and approach infinity in six dimensions. We use the droplet-scaling picture to show that the apparent nonzero value of α when L less then L^* should be 2θ, where θ is the domain wall energy scaling exponent. This formula is in reasonable agreement with the reported values of α.The dynamic magnetic susceptibility, χ(ω), of a model ferrofluid at a very low concentration (volume fraction, approximately 0.05%), and with a range of dipolar coupling constants (1≤λ≤8), is examined using Brownian dynamics simulations. With increasing λ, the structural motifs in the system change from unclustered particles, through chains, to rings. This gives rise to a nonmonotonic dependence of the static susceptibility χ(0) on λ and qualitative changes to the frequency spectrum. The behavior of χ(0) is already understood, and the simulation results are compared to an existing theory. The single-particle rotational dynamics are characterized by the Brownian time, τ_B, which depends on the particle size, carrier-liquid viscosity, and temperature. Temodal With λ≤5.5, the imaginary part of the spectrum, χ^”(ω), shows a single peak near ω∼τ_B^-1, characteristic of single particles. With λ≥5.75, the spectrum is dominated by the low-frequency response of chains. With λ≥7, new features appear at high frequency, which correspond to intracluster motions of dipoles within chains and rings. The peak frequency corresponding to these intracluster motions can be computed accurately using a simple theory.The long-term growth rate of populations in varying environments quantifies the evolutionary value of processing the information that biological individuals inherit from their ancestors and acquire from their environment. Previous models were limited to asexual reproduction with inherited information coming from a single parent with no recombination. We present a general extension to sexual reproduction and an analytical solution for a particular but important case, the infinitesimal model of quantitative genetics which assumes traits to be normally distributed. We study with this model the conditions under which sexual reproduction is advantageous and can evolve in the context of autocorrelated or directionally varying environments, mutational biases, spatial heterogeneities, and phenotypic plasticity. Our results generalize and unify previous analyses. We also examine the proposal made by Geodakyan that the presence of two phenotypically distinct sexes permits an optimal adaptation to varying environments. We verify that conditions exists where sexual dimorphism is adaptive but find that its evolutionary value does not generally compensate for the twofold cost of males.Numerous nanoscale studies that are related to harnessing photon energy focus on quantum effects. Thermodynamics analyses indicate the occurrence of a paradox for the standard model of the photocell with the power generated by a decay process. In order to measure the power accurately, a light-harvesting system connecting to Fermi contacts is proposed. Results show that the interference effect between different transition channels plays a decisive role in enhancing the power output of a photocell. The proposed model may provide a foundation for the future development of photoelectric converters.Competition between ion trapping and collisional detrapping is considered to be an important issue in the stabilization of the ion flow instability. The saturation amplitudes in terms of the particle density are derived and compared to the experimental data.The eigenstate thermalization hypothesis provides to date the most successful description of thermalization in isolated quantum systems by conjecturing statistical properties of matrix elements of typical operators in the (quasi)energy eigenbasis. Here we study the distribution of matrix elements for a class of operators in dual-unitary quantum circuits in dependence of the frequency associated with the corresponding eigenstates. We provide an exact asymptotic expression for the spectral function, i.e., the second moment of this frequency resolved distribution. The latter is obtained from the decay of dynamical correlations between local operators which can be computed exactly from the elementary building blocks of the dual-unitary circuits. Comparing the asymptotic expression with results obtained by exact diagonalization we find excellent agreement. Small fluctuations at finite system size are explicitly related to dynamical correlations at intermediate times and the deviations from their asymptotical dynamics. Moreover, we confirm the expected Gaussian distribution of the matrix elements by computing higher moments numerically.The ionic dynamic structure factor is examined to assess the relative roles of dissipation and the effective ionic interaction. Two disparate physically based models of dissipation, which can differ numerically by orders of magnitude, are used in molecular dynamics. We find a negligible impact on the amplitudes of the dynamic structure factors for physically realistic parameter values. We then examine the effective ionic interaction by varying its strength, the size of the atomic core (through a pseudopotential), and the screening model. We find that “diffusive” peaks in the dynamic structure factor are very sensitive to the form of the ionic interaction, and this sensitivity arises primarily from atomic physics through the pseudopotential. This suggests that it would be useful to employ the measured zero-frequency dynamic structure factor S_ii(k,0) as a constraint on the effective interaction, which in turn can be used to compute physical properties.