AAR-based decomposition algorithm for non-linear convex optimisation

We introduce a new method for a task of maximal material utilization, which is to fit a flexible, scalable three-dimensional body into another aiming for maximal volume whereas position and shape may vary. The difficulty arises from the containment constraint which is not easy to handle numerically. We use a collision detection method to check the constraint and reformulate the problem such that the constraint is hidden within the objective function. We apply methods from parametric optimization to proof that the objective function remains at least continuous. We apply the new approach to the problem of fitting a gemstone into a roughstone. For this previous approaches based on semi-infinite optimization exist, to which we compare our algorithm. The new algorithm is more suitable for necessary global optimization techniques and numerical results show that it works reliably and in general outperforms the previous approaches in both runtime and solution quality.     

Effective field theory for massive gravitons and gravity in theory space

We introduce a technique for restoring general coordinate invariance into theories where it is explicitly broken. This is the analog for gravity of the Callan-Coleman-Wess-Zumino formalism for gauge theories. We use this to elucidate the properties of interacting massless and massive gravitons. For a single graviton with a Planck scale M_Pl and a mass m_g, we find that there is a sensible effective field theory which is valid up to a high-energy cutoff Λ parametrically above m_g. Our methods allow for a transparent understanding of the many peculiarities associated with massive gravitons, among them the need for the Fierz-Pauli form of the Lagrangian, the presence or absence of the van Dam-Veltman-Zakharov discontinuity in general backgrounds, and the onset of non-linear effects and the breakdown of the effective theory at large distances from heavy sources. The natural sizes of all non-linear corrections beyond the Fierz-Pauli term are easily determined. The cutoff scales as Λ∼(m_g⁴M_Pl)^1/5 for the Fierz-Pauli theory, but can be raised to Λ∼(m_g²M_Pl)^1/3 in certain non-linear extensions. Having established that these models make sense as effective theories, there are a number of new avenues for exploration, including model building with gravity in theory space and constructing gravitational dimensions.     

Designing a New 4:2 Compressor Using an Efficient Multi-Layer Full-Adder Based on Nanoscale Quantum-Dot Cellular Automata

Quantum-dot Cellular Automata (QCA) is novel prominent nanotechnology. It promises a substitution to Complementary Metal–Oxide–Semiconductor (CMOS) technology with a higher scale integration, smaller size, faster speed, higher switching frequency, and lower power consumption. It also causes digital circuits to be schematized with incredible velocity and density. The full adder, compressor, and multiplier circuits are the basic units in the QCA technology. Compressors are an important class of arithmetic circuits, and researchers can use quantum compressors in the structure of complex systems. In this paper, first, a novel three-input multi-layer full-adder in QCA technology is designed, and based on it, a new multi-layer 4:2 compressor is presented. The proposed QCA-based full-adder and compressor uses an XOR gate. The proposed design offers good performance regarding the delay, area size, and cell number comparing to the existing ones. Also, in this gate, the output signal is not enclosed, and we can use it easily. The accuracy of the suggested circuits has been assessed with the utilization of QCADesigner 2.0.3. The results show that the proposed 4:2 compressor architecture utilizes 75 cell and 1.25 clock phases, which are efficient than other designs.

     

Nonlinear-forced vibrations of piezoelectrically actuated viscoelastic cantilevers

This paper aims to study the nonlinear-forced vibrations of a viscoelastic cantilever with a piecewise piezoelectric actuator layer on its top surface using the method of Multiple Scales. The governing equation of motion is a second-order nonlinear ordinary differential equation with quadratic and cubic nonlinearities which appear in stiffness, inertia, and damping terms. The nonlinear terms are due to the piezoelectricity, viscoelasticity, and geometry of the system. Forced vibrations of the system are investigated in the cases of primary resonance and non-resonance hard excitation including subharmonic and superharmonic resonances. Analytical expressions for frequency responses are derived, and the effects of different parameters including damping coefficient, thickness to width ratio of the beam, length and position of the piezoelectric layer, density of the beam, and the piezoelectric coefficient on the frequency-response curves are discussed for each case. It is shown that in all these cases, the response of the system follows a softening behavior due to the existence of the piezoelectric layer. The piezoelectric layer provides an effective tool for active control of vibration. In addition, the effect of the viscoelasticity of the beam on passive control of amplitude of vibration is illustrated.