DIGITAL FABRICATION AS A LEARNING MEDIA FOR LIGHTWEIGHT STRUCTURE WITH CASE STUDY OF SHELL STRUCTURE

The lightweight structure system is an effort to optimize the structure to distribute the load efficiently. Unfortunately, students often have difficulty imagining the learning outcomes application in the real world when studying light structural systems. However, the use of the scalar model can still explain several essential aspects of a lightweight structural system, one of which is the effect of connection and formation of material components on the structural capability. Therefore, this paper aims to bridge the learning process by utilizing digital devices from the concept stage of structural modeling with the help of software (Rhinoceros, Grasshopper, and Kangaroo) to the realization process using laser cutting. The method used is a semi-experimental method that applies Hooke's law principle, which produces a shell structure system with a digital fabrication approach that utilizes a lightweight material, namely, corrugated paper board, as the primary material. This paper concludes that digital technology and digital fabrication processes can help students understand the concept of lightweight structures because they can use computer simulations, cut them using laser cutting, and assemble them in the field in a series of simultaneous processes.

Using Multi-Group Invariance Analysis in Exploring Cross-Cultural Differences in Mathematics Anxiety: A Comparison of Australia and Russia

Mathematics anxiety is well known and studied concept. Most of the studies have been focused on the effects of mathematical anxiety on students’ academic achievement, especially from the viewpoint of analysing large national and international data sets. We aim to bring a different perspective to the existing research on mathematics anxiety and resilience by considering the measurement equivalence across cultures, so they can be compared fairly. We used Multi Group Invariance analysis with this purpose. Our findings suggested that full metric and partial scalar model invariance were confirmed which advise that the mathematics anxiety scale can be compared across two countries. We also ran multiple regression using Fisher’s Z to understand the reciprocal relationship among the variables across two samples. Preliminary results revealed that the perceived mathematics anxiety and perceived mathematics ability predict the measured mathematics anxiety equally well for both Australia and Russia.

The problem of normal oscillations of a viscous stratified fluid with an elastic membrane

Normal oscillations of a viscous stratified fluid partially filling an arbitrary vessel and bounded above by an elastic horizontal membrane are studied. In this case, we consider a scalar model problem that reflects the main features of the vector spatial problem. The characteristic equation for the eigenvalues of the model problem is obtained, the structure of the spectrum and the asymptotics of the branches of the eigenvalues are studied. Assumptions are made about the structure of the oscillation spectrum of a viscous stratified fluid bounded by an elastic membrane for an arbitrary vessel. It is proved that the spectrum of the problem is discrete, located in the right complex half-plane symmetrically with respect to the real axis, and has a single limit point $+\infty$. Moreover, the spectrum is localized in a certain way in the right half-plane, the location zone depends on the dynamic viscosity of the fluid.

Фононы и кроссовер Иоффе-Регеля в случайных решетках произвольной размерности

In the frame of the random matrix theory, it was shown, that the relaxation of the projection of the initial plane wave with the wave vector q is described by the equation of motion with the memory function which corresponds to the complex dynamical Young modulus E(ω). In the harmonic scalar model of displacements with the absence of energy dissipation, the Ioffe-Regel crossover arises universally in amorphous systems with the dimension d≥3. Vibrations above the Ioffe-Regel crossover are related to the diffusive nature and can be described by the diffusion equation with the damping Γ(q)∝ q².

Optical theorem and indefinite metric in λϕ4 delta-theory

A class of effective field theory called delta-theory, which improves ultraviolet divergences in quantum field theory, is considered. We focus on a scalar model with a quartic self-interaction term and construct the delta theory by applying the so-called delta prescription. We quantize the theory using field variables that diagonalize the Lagrangian, which include a standard scalar field and a ghost or negative norm state. As well known, the indefinite metric may lead to the loss of unitary of the [Formula: see text]-matrix. We study the optical theorem and check the validity of the cutting equations for three processes at one-loop order, and found suppressed violations of unitarity in the delta coupling parameter of the order of [Formula: see text].

Dirichlet boundary condition for the Lee–Wick-like scalar model

Lee–Wick-like scalar model near a Dirichlet plate is considered in this work. The modified propagator for the scalar field due to the presence of a Dirichlet boundary is computed, and the interaction between the plate and a point-like scalar charge is analysed. The non-validity of the image method is investigated and the results are compared with the corresponding ones obtained for the Lee–Wick gauge field and for the standard Klein–Gordon field.

Optimization of a mode-locked fiber laser based on nonlinear polarization rotation using genetic algorithm

Выполнено математическое моделирование волоконного лазера с синхронизацией мод на основе эффекта нелинейного вращения поляризации. Проведена оптимизация лазера с использованием генетического алгоритма. В результате были определены параметры лазерного резонатора, при которых достигается наибольшая энергия выходного импульса Purpose. The article addresses optimization of mode-locked fiber laser based on nonlinear polarization rotation. Determination of the resonator parameters corresponding to the single-pulse with the highest energy has been performed using the genetic algorithm. Metodology. Mathematical modelling has been carried out with the help of two models, namely, scalar and hybrid. Scalar model describes signal propagation by generalized nonlinear Schr¨odinger equation. Hybrid model describes section of DCF by pair of generalized nonlinear Schrodinger equations. Numerical simulation has been performed by the split-step Fourier method. Genetic algorithm has been implemented as SteadyState method by GALib library. The value of the fitness function is equal to the energy value for the single-pulse and otherwise zero. Findings. The genetic algorithm has been implemented for solving optimization problem of fiber lasers and modifying the algorithm to reduce the calculation time. The parameters of the laser for the scalar model are determined and agreement with the results obtained by the enumeration method is presented. For the hybrid model, a stable pulse with three times the energy was found. Conclusions. In this work, a determination of the optimal parameters for mode-locked fiber lasers based on nonlinear polarization rotation was presented. The problem was solved using a genetic algorithm. This is the first step towards creating a “smart” self-tuning laser

The Z5 model of two-component dark matter

Scenarios for multi-component scalar dark matter based on a single ZN (N ≥ 4) symmetry are simple and well-motivated. In this paper we investigate, for the first time, the phenomenology of the Z5 model for two-component dark matter. This model, which can be seen as an extension of the well-known singlet scalar model, features two complex scalar fields — the dark matter particles — that are Standard Model singlets but have different charges under a Z5 symmetry. The interactions allowed by the Z5 give rise to novel processes between the dark matter particles that affect their relic densities and their detection prospects, which we study in detail. The key parameters of the model are identified and its viable regions are characterized by means of random scans. We show that, unlike the singlet scalar model, dark matter masses below the TeV are still compatible with present data. Even though the dark matter density turns out to be dominated by the lighter component, we find that current and future direct detection experiments may be sensitive to signals from both dark matter particles.