Experimental magnetization curves for a polydisperse ferrofluid at various concentrations are examined using analytical theories and computer simulations with the aim of establishing a robust method for obtaining the magnetic-core diameter distribution function p(x). Theoretical expressions are fitted to the experimental data to yield the parameters of p(x). It is shown that the majority of available theories yield results that depend strongly on the ferrofluid concentration, even though the magnetic composition should be fixed. The sole exception is the second-order modified mean-field (MMF2) theory of Ivanov and Kuznetsova [Phys. Rev. E 64, 041405 (2001)] which yields consistent results over the full experimental range of ferrofluid concentration. To check for consistency, extensive molecular dynamics and Monte Carlo simulations are performed on systems with discretized versions of p(x) corresponding as closely as possible to that of the real ferrofluid. Essentially perfect agreement between experiment, theory, and computer simulation is demonstrated. In addition, the MMF2 theory provides excellent predictions for the initial susceptibility measured in simulations.

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Principal characteristics of interlayer interaction and relative motion of hexagonal boron nitride (h-BN) layers are investigated by the first-principles method taking into account van der Waals interactions. Dependences of the interlayer interaction energy on relative translational displacement of h-BN layers (potential energy surfaces) are calculated for two relative orientations of the layers, namely, for the layers aligned in the same direction and in the opposite directions upon relative rotation of the layers by 180 degrees. It is shown that the potential energy surfaces of bilayer h-BN can be approximated by the first Fourier components determined by symmetry. As a result, a wide set of physical qualintities describing relative motion of h-BN layers aligned in the same direction including barriers to their relative sliding and rotation, shear mode frequency and shear modulus are determined by a single parameter corresponding to the roughness of the potential energy surface, similar to bilayer graphene. The properties of h-BN layers aligned in the opposite directions are described by two such parameters. The possibility of partial and full dislocations in stacking of the layers is predicted for h-BN layers aligned in the same and opposite directions, respectively. The extended two-chain Frenkel-Kontorova model is used to estimate the width and formation energy of these dislocations on the basis of the calculated potential energy surfaces.

Exchange-correlation functionals with corrections for van der Waals interactions (PBE-D2, PBE-D3, PBE-D3(BJ), PBE-TS, optPBE-vdW and vdW-DF2) are tested for graphene and hexagonal boron nitride, both in the form of bulk and bilayer. The characteristics of the potential energy surface, such as the barrier to relative sliding of the layers and magnitude of corrugation, and physically measurable properties associated with relative in-plane and out-of-plane motion of the layers including the shear modulus and modulus for axial compression, shear mode frequency and frequency of out-of-plane vibrations are considered. The PBE-D3(BJ) functional gives the best results for the stackings of hexagonal boron nitride and graphite that are known to be ground-state from the experimental studies. However, it fails to describe the order of metastable states of boron nitride in energy. The PBE-D3 and vdW-DF2 functionals, which reproduce this order correctly, are identified as the optimal choice for general studies. The vdW-DF2 functional is preferred for evaluation of the modulus for axial compression and frequency of out-of-plane vibrations, while the PBE-D3 functional is somewhat more accurate in calculations of the shear modulus and shear mode frequency. The best description of the latter properties, however, is achieved also using the vdW-DF2 functional combined with consideration of the experimental interlayer distance. In the specific case of graphene, the PBE-D2 functional works very well and can be further improved by adjustment of the parameters.

Dislocations corresponding to a change of stacking in two-dimensional hexagonal bilayers, graphene and boron nitride, and associated with boundaries between commensurate domains are investigated using the two-chain Frenkel-Kontorova model on top of ab initio calculations. Structural transformations of bilayers in which the bottom layer is stretched and the upper one is left to relax freely are considered for gradually increased elongation of the bottom layer. Formation energies of dislocations, dislocation width and orientation of the boundary between commensurate domains are analyzed depending on the magnitude and direction of elongation. The second-order phase transition from the commensurate phase to the incommensurate one with multiple dislocations is predicted to take place at some critical elongation. The order parameter for this transition corresponds to the density of dislocations, which grows continuously upon increasing the elongation of the bottom layer above the critical value. In graphene and metastable boron nitride with the layers aligned in the same direction, where elementary dislocations are partial, this transition, however, is preceded by formation of the first dislocation at the elongation smaller than the critical one. The phase diagrams including this intermediate state are plotted in coordinates of the magnitude and direction of elongation of the bottom layer.

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Different DNA sequences have different physical properties, which seem to be important for their biological function. In particular, (dA)n.(dT)n has many unusual features, which include resistance to conformational changes in a variable chemical environment, an unusual thermodynamics of interaction with ligands, and the inability to reassociate into nucleosomes. Short A.T base-pair runs also play a critical role in DNA bending. It is believed that hydration of DNA is an important factor in determining the physical chemical and biological properties of different regions of DNA. Until now, however, it has not been possible to study the details of the hydration of DNA in dilute solution with sufficient sensitivity and precision. Moreover, it was not known if different base sequences differ in the extent of their hydration. Indirect evidence that (dA)n.(dT)n can be hydrated to a greater extent than other DNA sequences may be inferred from a recent study of the binding of drugs to polynucleotides. Here we used a novel high-precision technique measuring ultrasonic velocity to obtain direct estimates of the extent of hydration of various oligo- and polynucleotides in dilute solution. We report that different DNA sequences differ in their hydration, and that (dA)n.(dT)n in particular has an anomalously high level of hydration.