Inverse Engineering Method Research Articles

Dynamics of a driven open double two-level system and its entanglement generation

We investigate the dynamics of the driven open double two-level system by deriving a driven Markovian master equation based on the Lewis-Riesenfeld invariant theory. The transitions induced by coupling to the heat reservoir occur between the instantaneous eigenstates of the Lewis-Riesenfeld invariant. Therefore, different driving protocols associated with corresponding Lewis-Riesenfeld invariants result in different open system dynamics and symmetries. In particular, we show that since the instantaneous steady state of the driven double two-level system is one of eigenstates of the Lewis-Riesenfeld invariant at ultralow reservoir temperature, the inverse engineering method based on the Lewis-Riesenfeld invariants has a good performance in rapidly preparing the quantum state of open quantum systems. As an example, a perfect entangled state is generated by means of the inverse engineering method.

Shortcut to synchronization in classical and quantum systems

Synchronization is a major concept in nonlinear physics. In a large number of systems, it is observed at long times for a sinusoidal excitation. In this paper, we design a transiently non-sinusoidal driving to reach the synchronization regime more quickly. We exemplify an inverse engineering method to solve this issue on the classical Van der Pol oscillator. This approach cannot be directly transposed to the quantum case as the system is no longer point-like in phase space. We explain how to adapt our method by an iterative procedure to account for the finite-size quantum distribution in phase space. We show that the resulting driving yields a density matrix close to the synchronized one according to the trace distance. Our method provides an example of fast control of a nonlinear quantum system, and raises the question of the quantum speed limit concept in the presence of nonlinearities.

A stress-based shear fracture criterion considering the effect of stress triaxiality and Lode parameter

Failure in lightweight metal forming is a big challenge currently and prevents their widely application in weight reduction of automobile and aerospace structures. A stress-based shear ductile fracture criterion is introduced in this study to improve the prediction accuracy of failure for lightweight metals. The criterion (sDF2016) is developed based on the DF2016 criterion thereby endowing the criterion with the precise fracture predictability under wide stress states of shear, uniaxial tension, plane strain tension and equibiaxial tension. Besides, the criterion takes into account the stress state effect on fracture in a form of the stress triaxiality, the maximum shear stress and the Lode parameter. The sDF2016 criterion is also expected to be less sensitive to strain path changing effect because sDF2016 describe the onset of fracture in stress space. For the verification of the proposed sDF2016 criterion, the experiments are carried out for AA5182-O sheet with central hole, notched, in-plane shear and bulging specimens. Plastic deformation is accurately modeled by the Swift-Voce hardening law and the Drucker yield function. The sDF2016 criterion is then calibrated both by the direct and inverse engineering approaches, which is applied to predict fracture initiation under distinct stress states. The modeled result indicates that the calibrated sDF2016 criterion based on the inverse engineering method predicts the fracture stroke with a higher accuracy than the direct approach. The sDF2016 criterion is also used to depict fracture limits of AA2024-T351 alloy from compression to tension. The application shows that the proposed ductile fracture criterion is capable of modeling the fracture limits for sheet metals under various loading conditions from shear to plane strain tension.

Invariant-based investigation of shortcut to adiabaticity for quantum harmonic oscillators under a time-varying frictional force

We investigate the Shortcuts To Adiabaticity (STA) of a quantum harmonic oscillator under time-dependent frictional force, using invariant based inverse engineering method with a class of invariants characterized by a time-dependent frictional coefficient. We discuss the implementation of shortcut protocol in a generalized framework for any arbitrary time-dependent frictional interaction and study a class of such interaction from which the STA for the quantum harmonic oscillator can be obtained. We also discuss the application of the above protocol for the harmonic oscillator with time-varying mass. For an illustration, we consider the coupled photonic lattice as a harmonic oscillator with time-varying mass and frequency and discuss implementing the above protocol.

Mechanical Displacement for 3D Printers’ Parts Using FEM as Inverse Engineering Method in Honduras

Plastics industry is growing day by day; the new techniques generated by the fourth industrial revolution, such as additive manufacturing (AM) or better known as 3D printing, make the design and production of plastic products available to all. The aim of this research aims to explore the application of reverse engineering in improving the mechanical displacement in AM. The method used in this paper was the finite element analysis (FEM) applying it to different 3D printing parameters with a grid infill. Then the multiple line regression (MLR) was implemented to determine parameters relation. Finally, the simplex method to improve the parameters to decrease the mechanical displacement in AM. Reverse engineering process for parts that use 0.2 as shell wall and 25% of grid infill can have acceptable mechanical performance to be used in different applications.

Connection between Inverse Engineering and Optimal Control in Shortcuts to Adiabaticity.

We consider fast high-fidelity quantum control by using a shortcut to adiabaticity (STA) technique and optimal control theory (OCT). Three specific examples, including expansion of cold atoms from the harmonic trap, atomic transport by moving harmonic trap, and spin dynamics in the presence of dissipation, are explicitly detailed. Using OCT as a qualitative guide, we demonstrate how STA protocols designed from inverse engineering method can approach with very high precision optimal solutions built about physical constraints, by a proper choice of the interpolation function and with a very reduced number of adjustable parameters.

Strain hardening under large deformation for AA5182

In this study, an aluminium alloy of AA5182 is taken as the research object to study strain hardening under large plastic deformation. Tensile tests are done for four specimens, including dog-bone specimens, notched specimens, specimens with a central hole and in-plane shear specimens. Bulging tests are also conducted to measure strain hardening under balanced biaxial tension. In addition, an experimental method called in-plane torsion test is also used for shear loading. At least three experiments are completed for each type of specimens along the rolling direction (RD), diagonal direction (TD), and transverse direction (DD). The stroke of each tests is measured by a digital image correlation (DIC) system, and the load-stoke curves were obtained for the tests. Combined with an inverse engineering method, the strain hardening properties are calibrated for the alloy under different loading conditions of shear, uniaxial tension, plane strain tension, and balanced biaxial tension. The strain hardening under various loading conditions is compared and modelled by various yield functions to evaluate their performance. It is concluded that inverse engineering approach is a simple but powerful method to obtain the stress-strain curve up to large plastic deformation. It is also observed that it needs to develop yield functions to model yielding behaviour under complex loading conditions.

Engineered swift equilibration for Brownian objects: from underdamped to overdamped dynamics

We propose an enlarged framework to study transformations that drive an underdamped Brownian particle in contact with a thermal bath from an equilibrium state to a new one in an arbitrarily short time. To this end, we make use of a time and space-dependent potential, that plays a dual role: confine the particle, and manipulate the system. In the special case of an isothermal compression or decompression of a harmonically trapped particle, we derive explicit protocols that perform this quick transformation, following an inverse engineering method. We focus on the properties of these protocols, which crucially depend on two key dimensionless numbers that characterize the relative values of the three timescales of the problem, associated with friction, oscillations in the confinement and duration of the protocol. In particular, we show that our protocols encompass the known overdamped version of this problem and extend it to any friction for decompression and to a large range of frictions for compression.

Optical solitons in parity-time-symmetric mixed linear and nonlinear lattice with non-Kerr law nonlinearity

This work presents an analytical study of the existence of solitons in non-Kerr law media modulated by the PT-symmetric mixed linear and nonlinear optical complex lattices. Four types of non-Kerr law nonlinearity are taken into account and these are parabolic law, power law, dual-power law as well as polynomial law. With the aid of inverse engineering method, various families of solitons are reported. The presented results are important for describing the propagation of optical solitons in parity-time-symmetric lattices.

Reverse engineering of a nonlossy adiabatic Hamiltonian for non-Hermitian systems

We generalize the quantum adiabatic theorem to the non-Hermitian system and build a rigorous adiabaticity condition with respect to the adiabatic phase. The non-Hermitian Hamiltonian inverse engineering method is proposed for the purpose to adiabatically drive a artificial quantum state. For the sake of clearness, we take a concrete two-level system as an example to show the usefulness of the inverse engineering method. The numerical simulation result shows that our scheme can work well even under noise if the parameters are chosen appropriately. We can obtain the desired target state by adjusting extra rotating magnetic fields at a predefined time. Furthermore, certain noise and dissipation in the systems is no longer undesirable, but plays a positive role in our scheme. Therefore, our scheme could provide more choices for the realization of quantum-state engineering.

Optimal shortcuts to adiabaticity for a quantum piston

In this paper we use optimal control to design minimum-time adiabatic-like paths for the expansion of a quantum piston. Under realistic experimental constraints, we calculate the minimum expansion time and compare it with that obtained from a state of the art inverse engineering method. We use this result to rederive the known upper bound for the cooling rate of a refrigerator, which provides a quantitative description for the unattainability of absolute zero, the third law of thermodynamics. We finally point out the relation of the present work to the fast adiabatic-like expansion of an accordion optical lattice, a system which can be used to magnify the initial quantum state (quantum microscope).

Frictionless decompression in minimum time of Bose-Einstein condensates in the Thomas-Fermi regime

In this paper we study a fast adiabatic-like expansion of a one-dimensional Bose-Einstein condensate (BEC) in the Thomas-Fermi regime confined in a harmonic potential, using the theory of time-optimal control. We find that under reasonable assumptions suggested by the experimental setup, the minimum-time expansion occurs when the frequency of the potential changes in a bang-bang form between the permitted values. We calculate the necessary expansion time and compare it with that obtained using the state-of-the-art inverse engineering method under the same constraints. We also show that this minimum time scales logarithmically with the expansion factor for large values of the latter. This work is expected to find applications in areas where efficient manipulation of a BEC is of utmost importance, for example, in atom interferometry with a BEC.

Fast and Robust Spin Manipulation in a Quantum Dot by Electric Fields

We apply an invariant-based inverse engineering method to control, by time-dependent electric fields, the spin dynamics in a quantum dot with spin-orbit coupling in a weak magnetic field. The designed electric fields provide a shortcut to adiabatic processes that flip the spin rapidly, thus avoiding decoherence effects. This approach, being robust with respect to the device-dependent noise, can open new possibilities for spin-based quantum information processing.

Nature conservation information system in Slovenia

Purpose – The purpose of this paper is to describe the construction of the nature conservation information system in Slovenia, into which all official and more detailed data related to nature conservation will be integrated. The existing databases are to be replaced by a single base, which will diminish the possibility of errors occurring in data production, collection and distribution. The arrangement of data is transparent, their accessibility simple. Website data editing is enabled.Design/methodology/approach – On the basis of the existing databases analysis, an information system is constructed by the inverse engineering method. The database is organised per separate sets, where uniform codes are used. For web site users, the Nukleus graphical interface is built, which is connected with other information system components and enables web site data examination and processing.Findings – A modularly composed information system has been built, which establishes a uniform database, enables interoperability...

Shortcuts to quantum adiabatic processes

We review different ways to accelerate adiabatic processes in cold atom physics and atomic state preparation. Trap expansions or contractions and atomic transport may be accelerated by an invariant-based inverse engineering approach. Berry's inverse engineering method is also applied to produce fast versions of adiabatic passage methods.

Partially coupled anisotropic fracture model for aluminum sheets

The objective of the present paper is to incorporate the effect of plastic anisotropy on the fracture modeling of aluminum alloy 6061-T 6 sheets. Six different types of tests were performed to fracture, including tensile tests on classical dog-bone specimens, flat specimens with cutouts, plane strain grooved specimens, and punch indentation tests on circular blanks. A limited number of shear/tension tests on butterfly specimens were performed on a dual-actuator loading frame. Plastic properties were determined from the dog-bone tensile tests, and were verified by the remaining tests. It was found that the sheets exhibited little planar anisotropy but substantial out-of-plane anisotropy, characterized by the Lankford parameter, r. A comprehensive numerical analysis of the experiments revealed that the Hill 1948 quadratic anisotropic yield model is able to describe, with good accuracy, the plastic response of all five types of tests. Fracture surface strains were measured using a digital image correlation system. Average fracture strains were determined by measuring post-fracture thickness reduction. Local fracture strains were determined by means of an inverse engineering method involving matching the displacement to fracture from numerical simulations to those measured. Possible discrepancies between the magnitudes of the fracture strain in the three above methods are discussed. Based on the previous experience of the investigating team, the experimental fracture data were analyzed within the realm of the three-parameter Modified Mohr–Coulomb fracture model. Using the plane stress anisotropic plasticity equations, the calibrated fracture model was then transformed to the space of the equivalent strain to fracture and stress triaxiality. An alternative representation of the fracture locus in the space of principal strains was also constructed. Other important factors influencing the form of the fracture locus, such as mesh-size effect and solid versus shell representation, were also investigated.

An investigation of descaling spray on microstructural evolution in hot rolling

High pressure water spray is used to remove oxide scales in hot rolling of steel plate. This would reduce the temperature temporarily on the workpiece surface. To investigate the effect of temperature variation due to the descaling spray on the microstructural evolution, a thermal-mechanical coupled FE model has been established. The heat loss due to the spray is experimentally measured and modelled using the established FE model. The heat transfer coefficient is determined using an inverse engineering method. A set of unified viscoplastic constitutive equations is implemented into the commercial FE solver MARC through the user-defined subroutine CRPLAW. The effect of descaling water spray on the surface temperature variation is numerically studied. Furthermore, the effect of surface temperature variation on the evolution of dislocation density, recrystallisation and grain growth is investigated for various hot rolling conditions.