Similar sublattices of the root lattice A4A_4

Similar sublattices of the root lattice $A_4$ are possible, according to a result of Conway, Rains and Sloane, for each index that is the square of a non-zero integer of the form $m^2 + mn - n^2$. Here, we add a constructive approach, based on the arithmetic of the quaternion algebra $\mathbb{H} (\mathbb{Q} (\sqrt{5}))$ and the existence of a particular involution of the second kind, which also provides the actual sublattices and the number of different solutions for a given index. The corresponding Dirichlet series generating function is closely related to the zeta function of the icosian ring.Comment: 17 pages, 1 figure; revised version with several additions and improvement

What is moving in silica at 1 K? A computer study of the low-temperature anomalies

Though the existence of two-level systems (TLS) is widely accepted to explain low temperature anomalies in many physical observables, knowledge about their properties is very rare. For silica which is one of the prototype glass-forming systems we elucidate the properties of the TLS via computer simulations by applying a systematic search algorithm. We get specific information in the configuration space, i.e. about relevant energy scales, the absolute number of TLS and electric dipole moments. Furthermore important insight about the real-space realization of the TLS can be obtained. Comparison with experimental observations is included

Local Properties of the Potential Energy Landscape of a Model Glass: Understanding the Low Temperature Anomalies

Though the existence of two-level systems (TLS) is widely accepted to explain low temperature anomalies in the sound absorption, heat capacity, thermal conductivity and other quantities, an exact description of their microscopic nature is still lacking. We performed computer simulations for a binary Lennard-Jones system, using a newly developed algorithm to locate double-well potentials (DWP) and thus two-level systems on a systematic basis. We show that the intrinsic limitations of computer simulations like finite time and finite size problems do not hamper this analysis. We discuss how the DWP are embedded in the total potential energy landscape. It turns out that most DWP are connected to the dynamics of the smaller particles and that these DWP are rather localized. However, DWP related to the larger particles are more collective

Recovering non-Maxwellian particle velocity distribution functions from collective Thomson-scattered spectra

Collective optical Thomson scattering (TS) is a diagnostic commonly used to characterize plasma parameters. These parameters are typically extracted by a fitting algorithm that minimizes the difference between a measured scattered spectrum and an analytic spectrum calculated from the velocity distribution function (VDF) of the plasma. However, most existing TS analysis algorithms assume the VDFs are Maxwellian, and applying an algorithm which makes this assumption does not accurately extract the plasma parameters of a non-Maxwellian plasma due to the effect of non-Maxwellian deviations on the TS spectra. We present new open-source numerical tools for forward modeling analytic spectra from arbitrary VDFs, and show that these tools are able to more accurately extract plasma parameters from synthetic TS spectra generated by non-Maxwellian VDFs compared to standard TS algorithms. Estimated posterior probability distributions of fits to synthetic spectra for a variety of example non-Maxwellian VDFs are used to determine uncertainties in the extracted plasma parameters, and show that correlations between parameters can significantly affect the accuracy of fits in plasmas with non-Maxwellian VDFs

Fused filament fabrication: Comparison of methods for determining the interfacial strength of single welded tracks

The mechanical properties of plastic-based additively manufactured specimens have been widely discussed. However, there is still no standard that can be used to determine properties such as the interfacial strength of adjacent tracks and also to exclude the influence of varying manufacturing conditions. In this paper, a proposal is made to determine the interfacial strength using specimens with only one track within a layer. For this purpose, so-called single-wall specimens of polylactide were characterised under tensile load and the interfacial area between the adjacent layers was determined using three methods. It turned out that the determination of the interfacial area via the fracture surface is the most accurate method for determining the interfacial strength. The measured interfacial strengths were compared with the bulk material strength and it was found that the bulk material strength can be achieved under optimal conditions in the FFF process. It was also observed that with increasing nozzle temperature, the simultaneous printing of specimens influences the interfacial strength. To conclude, this method allows to measure the interfacial strength without superimposing the influence of voids. However, for example, the interfacial strength within a layer cannot be determined

Nudged Elastic Band calculation of the binding potential for liquids at interfaces

The wetting behavior of a liquid on solid substrates is governed by the nature of the effective interaction between the liquid-gas and the solid-liquid interfaces, which is described by the binding or wetting potential $g(h)$ which is an excess free energy per unit area that depends on the liquid film height $h$. Given a microscopic theory for the liquid, to determine $g(h)$ one must calculate the free energy for liquid films of any given value of $h$; i.e. one needs to create and analyze out-of-equilibrium states, since at equilibrium there is a unique value of $h$, specified by the temperature and chemical potential of the surrounding gas. Here we introduce a Nudged Elastic Band (NEB) approach to calculate $g(h)$ and illustrate the method by applying it in conjunction with a microscopic lattice density functional theory for the liquid. We show too that the NEB results are identical to those obtained with an established method based on using a fictitious additional potential to stabilize the non-equilibrium states. The advantages of the NEB approach are discussed.Comment: 5 pages, 2 figure

On the Creation and Optical Microstructure Characterisation of Additively Manufactured Foam Structures (AMF)

Plastic-based additive manufacturing processes are becoming increasingly popular in the production of structural parts. Based on the idea of lightweight design and the aim of extending the functionality of additive structures, the production of additively manufactured foam structures has emerged as a new field of application. The optical characterisation of these structures is of particular importance for process adjustments and the identification of (unwanted) changes in the foam structure. The degree of foaming and the fineness of a foam structure are of interest at this point. In this context, only the part of a structure dominated by foam pores is considered a foam structure. So far, there are no sophisticated methods for such an optical characterisation. Therefore, in this work, microscope images of manufactured as well as artificially created additively manufactured foam structures were evaluated. On these images, the features porosity, pore size, pore amount and a measure for the textural change were determined in order to obtain information about changes within an additively manufactured foam structure. It is shown that additive structures show changing pore shapes depending on the orientation of the cutting plane, although there are no changes in the foaming behaviour. Therefore, caution is required when identifying changes within the foam structure. It was also found that, owing to the additive process, the total porosity is already set in the slicing process and remains constant even if the degree of foaming of individual tracks is changed. Therefore, the degree of foaming cannot be determined on the basis of the total porosity, but it can be assessed on the basis of the formation of large networks of process-related pores

Can different parameter sets lead to equivalent optima between geometric accuracy and mechanical properties in Arburg plastic freeforming?

Technological advances have led to the increased use of plastic-based additive manufacturing processes for the production of consumer goods and spare parts. For this reason, the need for the best possible mechanical properties while maintaining geometric accuracy is becoming increasingly important. One of these additive manufacturing processes is the Arburg Plastic Freeforming process, which differs from the widely used Fused Filament Fabrication process in the way that droplets are discharged along a track instead of continuous extruded tracks. As with all other plastic-based additive manufacturing processes, due to the round shape of the tracks, voids occur between the individual tracks during manufacturing, which effects mechanical properties. In contrast to previous work, which mainly focused on how the mechanical properties change with a change in a single printing parameter, this work focused more closely on the interaction of three relevant printing parameters considered as a parameter set. Their influence on the mechanical properties was investigated by tensile tests, the influence on the residual porosity by density measurements and the influence on the geometric accuracy by surface roughness measurements. It was shown that by considering the parameters as a parameter set, states of high density and therefore high mechanical properties while reaching minimal surface roughness can be achieved for significantly more combinations than previously assumed. However, for these states the residual porosity was slightly different. This difference was explained by a parameter-dependent deformation factor of the droplets, which influences the maximal possible degree of filling during manufacturing. For the optimization of arbitrary parameter sets, an analytical model was derived

On the creation and optical microstructure characterisation of additively manufactured foam structures (AMF)

Plastic-based additive manufacturing processes are becoming increasingly popular in the production of structural parts. Based on the idea of lightweight design and the aim of extending the functionality of additive structures, the production of additively manufactured foam structures has emerged as a new field of application. The optical characterisation of these structures is of particular importance for process adjustments and the identification of (unwanted) changes in the foam structure. The degree of foaming and the fineness of a foam structure are of interest at this point. In this context, only the part of a structure dominated by foam pores is considered a foam structure. So far, there are no sophisticated methods for such an optical characterisation. Therefore, in this work, microscope images of manufactured as well as artificially created additively manufactured foam structures were evaluated. On these images, the features porosity, pore size, pore amount and a measure for the textural change were determined in order to obtain information about changes within an additively manufactured foam structure. It is shown that additive structures show changing pore shapes depending on the orientation of the cutting plane, although there are no changes in the foaming behaviour. Therefore, caution is required when identifying changes within the foam structure. It was also found that, owing to the additive process, the total porosity is already set in the slicing process and remains constant even if the degree of foaming of individual tracks is changed. Therefore, the degree of foaming cannot be determined on the basis of the total porosity, but it can be assessed on the basis of the formation of large networks of process-related pores