The roughness of crack interfaces is reported in quasistatic fracture, using an elastic network of beams with random breaking thresholds. For strong disorders we obtain zeta = 0.86(3) for the roughness exponent, a result which is very different from the minimum energy surface exponent, i.e., zeta = 2 / 3. A crossover to lower values is observed as the disorder is reduced, the exponent in this regime being strongly dependent on the disorder.

In calculations for liquid 4 He, an investigation is made to check the accuracy of a lowestorder constrained variational (LOCV) method, using modified "healing" conditions on the two-body Jastrow wave function. Results obtained for the ground-state energy for four different interaction models are fitted by a polynomial expression, whereby the pressure, compressibility and velocity of first sound are obtained. The theoretical results are found to be in fair agreement with experimental results.PACS number(s): 67.20.+k, 67.40.Mj

A lowest-order constrained variational (LOCV) method, with modified conditions of healing on the two-body Jastrow wave function, is investigated in calculations for the ground-state energy levels of many-body spin-polarized atomic deuterium. Results are obtained for the , and phases, corresponding to equal occupations of one, two or three nuclear spin states. Estimates for the optimum healing conditions are obtained by comparison of LOCV results with current Monte Carlo benchmarks. The nature of the phases, i.e., quantum gas or quantum liquid, is discussed, the energy of the phase in our calculations always occurring above the gas-liquid interphase for healing conditions within a physically acceptable range.

We study the effects realistic fracture criteria have on crack morphology obtained in numerical simulations with a stochastic discrete element method. Results are obtained with two criteria which are consistent with the theory of elasticity and compared with previous results using the original criterion, chosen when the method was first published. The conventional choice has been to consider the combined loading as an interaction between bending and tensile forces only, leaving out shear forces altogether. Moreover the combination of bending and tension used in the old criterion is correct only for plastic deformations. Our results show that the inclusion of shear forces have a profound effect on crack morphology. We consider two types of external loading, torsion applied to a circular cylinder and tension applied to a cube. In the tensile case, the exponent which characterises scaling of crack roughness with system size is found to be very close to the experimental value ζ ∼ 0.5 when realistic fracture criteria are used. In the present calculations we obtain ζ = 0.52, a value which remains constant for all disorders. It is proposed that the small-scale exponent ζ = 0.8 appears as a consequence of cleavage between crystal planes and consequently requires a different fracture criterion than that which is used on larger scales. PACS numbers: 81.40.Np, 62.20.mt, 05.40.-a arXiv:1808.06245v1 [cond-mat.soft]

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