Investigating The Load-Bearing Capacity Of Additively Manufactured Lattice Structures

Additive manufacturing provides unprecedented design freedom from the product’s external appearance to the internal structure. Additively manufactured parts, objects can be designed with cellular lattice structures as infills. The application of lattice structures can reduce the required amount of material and desired properties can be assigned to certain objects. There are several different lattice structures each with its own unique, exclusive property or properties. In this study a wide spectrum of so called ‘auxetic’ and standard lattice structures will be compared using finite element method and compression laboratory tests. The considered auxetic and non-auxetic cellular structures are based on the result of other researches. Along with the aforementioned existing lattices several new structures were proposed. Nine distinct additively manufactured specimens were compared.

Contribution of the Multiplicity Fluctuation in the Temperature Dependence of Phonon Spectra of Rare-Earth Cobaltites

We have studied, both experimentally and theoretically, the unusual temperature dependence of the phonon spectra in NdCoO3, SmCoO3 and GdCoO3, where the Co3+ ion is in the low-spin (LS) ground state, and at the finite temperature, the high-spin (HS) term has a nonzero concentration nHS due to multiplicity fluctuations. We measured the absorption spectra in polycrystalline and nanostructured samples in the temperature range 3–550 K and found a quite strong breathing mode softening that cannot be explained by standard lattice anharmonicity. We showed that the anharmonicity in the electron–phonon interaction is responsible for this red shift proportional to the nHS concentration.

Rigidity at infinity for lattices in rank-one Lie groups

Let [Formula: see text] be a non-uniform lattice in [Formula: see text] without torsion and with [Formula: see text]. By following the approach developed in [S. Francaviglia and B. Klaff, Maximal volume representations are Fuchsian, Geom. Dedicata 117 (2006) 111–124], we introduce the notion of volume for a representation [Formula: see text] where [Formula: see text]. We use this notion to generalize the Mostow–Prasad rigidity theorem. More precisely, we show that given a sequence of representations [Formula: see text] such that [Formula: see text], then there must exist a sequence of elements [Formula: see text] such that the representations [Formula: see text] converge to a reducible representation [Formula: see text] which preserves a totally geodesic copy of [Formula: see text] and whose [Formula: see text]-component is conjugated to the standard lattice embedding [Formula: see text]. Additionally, we show that the same definitions and results can be adapted when [Formula: see text] is a non-uniform lattice in [Formula: see text] without torsion and for representations [Formula: see text], still maintaining the hypothesis [Formula: see text].

Standard Lattice-Based Key Encapsulation on Embedded Devices

Lattice-based cryptography is one of the most promising candidates being considered to replace current public-key systems in the era of quantum computing. In 2016, Bos et al. proposed the key exchange scheme FrodoCCS, that is also a submission to the NIST post-quantum standardization process, modified as a key encapsulation mechanism (FrodoKEM). The security of the scheme is based on standard lattices and the learning with errors problem. Due to the large parameters, standard latticebased schemes have long been considered impractical on embedded devices. The FrodoKEM proposal actually comes with parameters that bring standard lattice-based cryptography within reach of being feasible on constrained devices. In this work, we take the final step of efficiently implementing the scheme on a low-cost FPGA and microcontroller devices and thus making conservative post-quantum cryptography practical on small devices. Our FPGA implementation of the decapsulation (the computationally most expensive operation) needs 7,220 look-up tables (LUTs), 3,549 flip-flops (FFs), a single DSP, and only 16 block RAM modules. The maximum clock frequency is 162 MHz and it takes 20.7 ms for the execution of the decapsulation. Our microcontroller implementation has a 66% reduced peak stack usage in comparison to the reference implementation and needs 266 ms for key pair generation, 284 ms for encapsulation, and 286 ms for decapsulation. Our results contribute to the practical evaluation of a post-quantum standardization candidate.

Recent progress in applying lattice QCD to kaon physics

Standard lattice calculations in kaon physics are based on the evaluation of matrix elements of local operators between two single-hadron states or a single-hadron state and the vacuum. Recent progress in lattice QCD has gone beyond these standard observables. I will review the status and prospects of lattice kaon physics with an emphasis on non-leptonic K → ππ decay and long-distance processes including K0-K0 mixing and rare kaon decays.

Approximation viscosity of one-parameter families of lattice Boltzmann equations

Рассматриваются свойства параметрических решеточных схем Больцмана. С использованием метода Чепмена--Энскога из дифференциального приближения схем получена система уравнений относительно гидродинамических переменных и выведено выражение для аппроксимационной вязкости. Показано, что существует численная вязкость, которую необходимо учитывать при проведении расчетов. Необходимые условия устойчивости получены из условия неотрицательности выражения для аппроксимационной вязкости. При решении тестовой задачи о течении в каверне с подвижной крышкой показано, что возможно проведение расчетов по параметрическим схемам в случаях, когда неприменимо обычное решеточное уравнение Больцмана. A number of properties of parametric lattice Boltzmann schemes are considered. The Chapman-Enskog method is used to derive a system of equations for hydrodynamic variables and to obtain an expression for the approximation viscosity from the differential approximation of the schemes. It is shown that there exists the numerical viscosity that should be taken into account during numerical computations. Necessary stability conditions are obtained from the nonnegativity condition for the approximation viscosity. The possibility of computations using the proposed schemes is demonstrated by the numerical solution of the lid-driven cavity flow problem when the standard lattice Boltzmann equation is inapplicable.