Mutual information in classical spin models

The total many-body correlations present in finite temperature classical spin systems are studied using the concept of mutual information. As opposed to zero-temperature quantum phase transitions, the total correlations are not maximal at the phase transition, but reach a maximum in the high temperature paramagnetic phase. The Shannon and Renyi mutual information in both Ising and Potts models in 2 dimensions are calculated numerically by combining matrix product states algorithms and Monte Carlo sampling techniques

Development and validation of a high constraint modified boundary layer finite element model

When a notched structure is loaded, its behaviour is not only affected by the material properties but also by the geometry (of both the structure and the defect) and loading condition, alternatively termed as constraint condition. Therefore, the relation between the failure behaviour of a small scale fracture mechanics test and a full scale structure needs to be elucidated. In an attempt to understand and describe such relationships, the crack tip stress fields are analysed by means of finite element simulations and compared for several test specimen geometries. A reference for comparison is the crack tip stress field obtained from a high constraint reference geometry, further called a modified boundary layer model. First, this article provides some theoretical background on the modified boundary layer model. Second, the development of a 2D model is outlined in detail, focussing on the mesh design in the vicinity of the crack tip and the applied boundary conditions. Afterwards, an analytical and numerical validation is provided, based on the level of the applied load and, on the other hand, on the magnitude of the crack tip stress fields. Finally, this validated model is used for the comparison of several constraint parameters. This comparison indicates a weak influence of the T-stress on the Q-parameter for positive T-stresses. In contrast, negative T-stresses result in more pronounced negative Q-values

Renormalization group flows of Hamiltonians using tensor networks

A renormalization group flow of Hamiltonians for two-dimensional classical partition functions is constructed using tensor networks. Similar to tensor network renormalization ([G. Evenbly and G. Vidal, Phys. Rev. Lett. 115, 180405 (2015)], [S. Yang, Z.-C. Gu, and X.-G Wen, Phys. Rev. Lett. 118, 110504 (2017)]) we obtain approximate fixed point tensor networks at criticality. Our formalism however preserves positivity of the tensors at every step and hence yields an interpretation in terms of Hamiltonian flows. We emphasize that the key difference between tensor network approaches and Kadanoff's spin blocking method can be understood in terms of a change of local basis at every decimation step, a property which is crucial to overcome the area law of mutual information. We derive algebraic relations for fixed point tensors, calculate critical exponents, and benchmark our method on the Ising model and the six-vertex model.Comment: accepted version for Phys. Rev. Lett, main text: 5 pages, 3 figures, appendices: 9 pages, 1 figur

Design of a (mini) wide plate specimen for strain-based weld integrity assessment

Wide plate tension tests are commonly executed to investigate the integrity of defective welds under a uniaxial load. The specimen can be flat or curved, depending on the geometry from which it has been extracted (plate or pipe). Despite its usefulness, the design of the (curved) wide plate test is still not standardized up-to-date. This paper compares two specimen designs with a different length-to-width ratio through finite element analysis, using a design-of-experiments approach to account for different influential factors. The results reveal significant differences between the interpretation of tests with net section collapse and gross section collapse, promoted by weld strength overmatch. Further, both investigated designs tend to provide similar estimates of failure mode, strain capacity and crack driving force. Hence, the shorter specimen is considered an acceptable alternative to the slightly more representative longer specimen

Influence and evaluation of constraint on fracture toughness in pipeline research

Accessing nowadays fossil fuel reserves requires a strain-based design approach. Within such design, the ductile tearing resistance is a key parameter in assessing the defect tolerance. To determine this tearing resistance, full scale (pressurized) tests can be performed. However, such approach would be costly and time consuming. Consequently, effort is made to select appropriate small scale test specimens. Most research has focused so far on the single edge notch bend (SENB) and tensile (SENT) specimen. To evaluate the suitability of these test specimens, the crack tip stress fields can be examined or the resistance curves compared with full scale structures. This paper aims at comparing the trends observed using these techniques. Furthermore, the suitability of the small scale test specimens is evaluated. It is concluded that sufficiently long (length-to-width ratio equal to ten) clamped SENT specimens have the potential to predict the tearing resistance of full scale pipes. In addition, the internal pressure does not significantly affect the fracture toughness. These conclusions are stated by both experimental results and finite element simulations

Validation of a finite element model for fracture mechanics specimens

Single parameter formulations have shown to be insufficient to describe constraint effects in fracture mechanics specimens. This has lead researchers to a two parameter approach like the J-Q theory. In order to investigate constraint effects, the authors have developed a generic finite element model. Prior to drawing conclusions this model must first be validated, which is the topic of this paper. This validation has been done by comparing analytical expressions of the J-integral with those obtained from the performed simulations. The compared geometries were center cracked tension (CCT) and double edge notched tension (DENT) fracture mechanics specimens. The results showed good agreement with the analytical expressions and, as such, the model can now be confidently applied to determine values of the J-integral. This is a first step towards evaluating two parameter J-Q constraint

Investigation of strain measurements in (curved) wide plate specimens using digital image correlation and finite element analysis

Some pipelines face global plastic straining due to the nature of their installation process or harsh environmental conditions during operation. The ability of the girth welds to withstand these plastic strains is often evaluated on the basis of wide plate tests. Key for the validity of these tests is a representative measurement of remote strain, mostly obtained by linear variable differential transformers and/or strain gauges. The outcome of the remote strain measurement depends on the specimen geometry and the position of these sensors. In an attempt to investigate a specific geometric design of wide plate specimens and to find appropriate remote strain sensor positions, the authors have performed a series of tension tests on medium-sized wide plate specimens, supported by digital image correlation strain measurements. In addition, finite element simulations have been performed to evaluate whether the experimental observations can be extrapolated to a wider range of conditions. The results indicate that the strain distribution is mostly influenced by the weld strength mismatch, which governs the lateral restraint. For all experiments and simulations, nevertheless, the strain field was highly uniform in an identified zone, resulting in simple guidelines regarding specimen geometry and sensor positioning

Matrix product state renormalization

The truncation or compression of the spectrum of Schmidt values is inherent to the matrix product state (MPS) approximation of one-dimensional quantum ground states. We provide a renormalization group picture by interpreting this compression as an application of Wilson's numerical renormalization group along the imaginary time direction appearing in the path integral representation of the state. The location of the physical index is considered as an impurity in the transfer matrix and static MPS correlation functions are reinterpreted as dynamical impurity correlations. Coarse-graining the transfer matrix is performed using a hybrid variational ansatz based on matrix product operators, combining ideas of MPS and the multi-scale entanglement renormalization ansatz. Through numerical comparison with conventional MPS algorithms, we explicitly verify the impurity interpretation of MPS compression, as put forward by [V. Zauner et al., New J. Phys. 17, 053002 (2015)] for the transverse-field Ising model. Additionally, we motivate the conceptual usefulness of endowing MPS with an internal layered structure by studying restricted variational subspaces to describe elementary excitations on top of the ground state, which serves to elucidate a transparent renormalization group structure ingrained in MPS descriptions of ground states.Comment: 15 pages, 10 figures, published versio