General Theoretical Scheme Research Articles

High‐Throughput Fabrication of Curved Plasmonic Metasurfaces for Switchable Beam Focusing and Thermal Infrared Cloaking

AbstractConsiderable effort is devoted to research on reconfigurable beam focusing and optical cloaking in the basis of metamaterials/metasurfaces. However, it remains a great challenge to achieve multifunctional wavefront control on curved platforms, especially in the reflective case, which is of paramount importance in the emerging fields of active optics and stealth research. This study proposes a novel strategy to control the versatile reflective structured wavefront on a conformal platform by curving a flexible metasurface. This metasurface is fabricated in a high‐throughput manner by using ultra‐violet nano‐imprinting lithography (UV‐NIL), and its efficacy is verified through consistent simulated and experimental results. The conformal metasurface is designed to realize multifunctional performance by employing all‐metallic plasmonic structures based on the Pancharatnam‐Berry (PB) phase. A general theoretical scheme is also proposed for the projection of a curved surface onto a reference plane by a judicious compensation, combining the geometrical PB phase with curvature‐induced propagation phase. Moreover, as a proof‐of‐concept, curved metasurfaces with cylindrical shapes are experimentally characterized by their multifunctionalities in generating a beam spot with a continuously tunable focal length and reflecting plane waves used for camouflage, thereby confirming the feasibility and effectiveness of the proposed strategy.

Stationary states of a dissipative two-qubit quantum channel and their applications for quantum machine learning

Entangled-state preparation and preservation are the cornerstones of any quantum information platform. However, the strongest adversaries in quantum information science are unwanted environmental effects such as decoherence and dissipation. Here, we address how to control and harness these unwanted effects that arise from the coupling of a system with its environment, to provide stationary entangled states for quantum machine learning (QML). To do so, we design a dissipative quantum channel, i.e., a two-qubit system interacting with a squeezed vacuum field reservoir, and study the output state of the channel by solving the corresponding master equation, especially, in the small squeezing regime. We show that the time-dependent output state of the channel is the so-called two-qubit X-states that generalize many families of entangled two-qubit states. Also, by considering a general Bell diagonal state as the initial state of the system, we reveal that this dissipative channel generates two well-known classes of entangled mixed state and Werner-like states in the steady-state regime. Moreover, this channel provides an efficient way to determine whether a given initial state results in a stationary entangled state or not. Finally, we examine the potential application of the designed two-qubit channel for QML. In this line, we propose a general theoretical scheme for quantum neural networks (QNNs) implemented with the variational quantum circuits, which encode data in continuous variables (CVs) of the two-qubit states. The linear (also referred to as affine) and nonlinear (activation function) transformations are enacted in the QNN using the stationary states of the two-qubit channel and measurement process, respectively. Finally, we proceed to test our proposed model by solving some supervised binary classification tasks. Integrating the non-unitary transformation and parallel-processed neural computing on such a two-qubit channel establishes the requirements for a meaningful QNN. Such a CV-QNN model with sufficient layers may execute any algorithm implementable on a universal CV quantum computer.

A general theoretical scheme for shape-programming of incompressible hyperelastic shells through differential growth

In this paper, we study the problem of shape-programming of incompressible hyperelastic shells through differential growth. The aim of the current work is to determine one of the possible growth tensors (or growth functions) that can produce the deformation of a shell to the desired shape. First, a consistent finite-strain shell theory is introduced. The shell equation system is established from the 3D governing system through a series expansion and truncation approach. Based on the shell theory, the problem of shape-programming is studied under the stress-free assumption. For a special case in which the parametric coordinate curves generate a net of curvature lines on the target surface, the sufficient condition to ensure the vanishing of the stress components is analyzed, from which the explicit expression of the growth tensor can be derived. In the general case, we conduct the variable changes and derive the total growth tensor by considering a two-step deformation of the shell. With these obtained results, a general theoretical scheme for shape-programming of thin hyperelastic shells through differential growth is proposed. To demonstrate the feasibility and efficiency of the proposed scheme, several typical examples are studied. The derived growth tensors in these examples have also been implemented in the numerical simulations to verify their correctness and accuracy. The simulation results show that the target shapes of the shell samples can be recovered completely. The scheme for shape-programming proposed in the current work is helpful in designing and manufacturing intelligent soft devices.

Human Movement: In Search of Borderlands Between Philosophy and Physics

In this essay, we adopt a theory of behavior developed by the French philosopher Maurice Merleau-Ponty in an attempt to find common ground between philosophy and physics. We look for ways to reconcile matter with meaning, physical motion with the principles of ethics, body with mind. We proceed in three steps, first by providing a review of Merleau-Ponty’s theory; second by showing how ethical behavior is constrained and shaped by factors found in physics, chemistry, and biology; and, finally, by describing how physical motion is affected by factors that transcend the laws of classical physics. For the latter purpose, we accept a theory of parametric control of movements with spatial referent coordinates. Our purpose is not to solve specific problems of motor control or moral decision making but, rather, to test a general theoretical scheme that carries a number of practical implications for both research and education, including the need for collaboration between and among diverse research subdisciplines in kinesiology.

Methodology of information support of studies and works on different-scale forecasting oil and gas fields

The generalized statement of theoretical principles of information support of R&D on forecasting and development of oil and gas fields of various geological and genetic types corresponding to modern challenges of objective factors of growth of technical complexity and geological prospecting, exploration and operational works cost is presented.
 The main working tool is a targeted multi-scale information modeling of promising geological objects, based on the general theoretical scheme of forecast-paleoreconstructive retrospective-static model with the introduction of the concept of formation-material system of oil and gas accumulation, which includes three cognitive-functional components: initial source, transportation and objects of hydrocarbons localization.
 This methodological apparatus provides solutions to the main forecasting and diagnostic tasks: development of localization criteria, forecasting of traps and assessment of the potential of their hydrocarbons realization. The proposed apparatus is multi-scale, i.e. one that provides forecasting at the zonal (group of deposits), local (deposits) and sublocal (productive beds) levels.
 Prospects for further development of the direction are to develop a modern holistic theory of geoinformatic modeling and its subject methodological and methodological section – frame organization of the geological environment of oil and gas specialization in order to innovatively increase the efficiency of hydrocarbon field development. The examples of updated target information modeling of promising geological objects, basing upon methodological approach of infogeology with introducing of geological environment frame organization principles are demonstrated. As an object of modeling the regional formational complex of Tournaisian-Visean oil-gas horizon of the Dniprovsko-Donetska depression is considered. The solution of tasks, connected with this problem, comprises: the revision of initial data for innovative presenting of geoinformation modeling; defining of selected geological objects frame organization (structure); development of different scale promising geological objects frames and their transformation into geoinformatic format; preparing of recommendations for promising geological objects of different scales (zonal, local, sublocal) basing upon pertinent geoinformatic models. The expected result of this methodology introducing is to obtain innovative technology of information supervision for R&D aimed at efficient development of oil and gas fields.

Can a nonextremal black hole be a particle accelerator?

We consider particle collisions in the background of a nonextremal black hole. Two particles fall from infinity, particle 1 is fine-tuned (critical), collision occurs in its turning point. The first example is the Reissner-Nordstr\"{o}m (RN) one. If the energy at infinity $E_{1}$ is big enough, the turning point is close to the horizon. Then, we derive a simple formula according to which $E_{c.m.}\sim E_{1}\kappa ^{-1/2}$, where $\kappa $ is a surface gravity. Thus significant growth of $E_{c.m.}$ is possible if (i) particle 1 is ultrarelativistic (if both particles are ultrarelativistic, this gives no gain as compared to collisions in flat space-time), (ii) a black hole is near-extremal (small $\kappa $). In the scenario of multiple collisions the energy $E_{c.m.}$ is finite in each individual collision. However, it can grow in subsequent collisions, provided new near-critical particles are heavy enough. For neutral rotating black holes, in case (i) a turning point remains far from the horizon but large $E_{c.m.}$ is still possible. Case (ii) is similar to that for collisions in the RN metric. We develop a general theoretical scheme, direct astrophysical applications can be a next step to be studied.

Strain gradient nonlocal Biot poromechanics

Experimental observation demonstrates that both negative and positive dispersion relations are possible for porous media, which classical Biot theory fails to predict and interpret. The present paper establishes a higher-order strain gradient nonlocal poroelasticity considering both the size effects and heterogeneity structure effects to describe the specific physical characteristics of material and structure for porous media. The theoretical frame of Biot theory is reserved, and two length parameters, nonlocal parameter and scale factor are introduced to improve the classical Biot theory. Such an amendment yields remarkable merits as compared with the classical Biot theory because the nonlocality considers interactions among the solid grains with different sizes, while the high-order poromechanics only consider the locality of strain field. The differential-form constitutive relation and the governing equations of motion associated with boundary conditions are proposed by using variational method. The theory is finally applied to analyze the wave propagation characteristics in porous media, on which based both negative and positive dispersion relations as observed in the experiments can be successfully reproduced. The essential mechanism of softening and hardening effects in porous media is the result of competition of scale factor and nonlocal parameter. Thus, this higher-order strain gradient nonlocal poroelasticity is a general and complete theoretical scheme, which is capable of interpreting dynamical behaviors of porous media in a wide frequency of range.

Theory of coherent-oscillations generation in terahertz pump-probe spectroscopy: From phonons to electronic collective modes

Time-resolved spectroscopies using intense THz pulses appear as a promising tool to address collective electronic excitations in condensed matter. In particular recent experiments showed the possibility to selectively excite collective modes emerging across a phase transition, as it is the case for superconducting and charge-density-wave (CDW) systems. One possible signature of these excitations is the emergence of coherent oscillations of the differential probe field in pump-probe protocols. While the analogy with the case of phonon modes suggests that the basic underlying mechanism should be a sum-frequency stimulated Raman process, a general theoretical scheme able to describe the experiments and to define the relevant optical quantity is still lacking. Here we provide this scheme by showing that coherent oscillations as a function of the pump-probe time delay can be linked to the convolution in the frequency domain between the squared pump field and a Raman-like non-linear optical kernel. This approach is applied and discussed in few paradigmatic examples: ordinary phonons in an insulator, and collective charge and Higgs fluctuations across a superconducting and a CDW transition. Our results not only account very well for the existing experimental data in a wide variety of systems, but they also offer an useful perspective to design future experiments in emerging materials.

Relativistic theory of electron-nucleus-radiation coupled dynamics in molecules: Wavepacket approach.

We propose a general theoretical scheme of relativistic electron-nucleus coupled dynamics of molecules in radiation fields, which is derived from quantum electrodynamical formalism. Aiming at applications to field-induced dynamics in ultrastrong laser pulses to the magnitude of 1016 W/cm2 or even larger, we derive a nonperturbative formulation of relativistic dynamics using the Tamm-Dancoff expansion scheme, which results in, within the lowest order expansion, a time-dependent Schrödinger equation with the Coulombic and retarded transversal photon-exchange interactions. We also discuss a wavepacket type nuclear dynamics adapted for such dynamics.

Transmission of electromagnetic beam through a uniaxial anisotropic slab

We present a general theoretical scheme to investigate the propagation characteristics of a focused electromagnetic beam in a uniaxial anisotropic slab. The reflected, internal as well as transmitted waves are expanded in terms of cylindrical vector wave functions, and the unknown expansion coefficients are determined by virtue of the boundary conditions and the projection method. For incidence of a fundamental Gaussian beam, Hermite–Gaussian beam and doughnut mode beam, normalized field intensity distributions are evaluated and discussed briefly.

Tail state formation in solar cell materials: First principles analyses of zincblende, chalcopyrite, kesterite, and hybrid perovskite crystals

Tail state formation in solar cell absorbers leads to a detrimental effect on solar cell performance. Nevertheless, the characterization of the band tailing in experimental semiconductor crystals is generally difficult. In this article, to determine the tail state generation in various solar cell materials, we have developed a quite general theoretical scheme in which the experimental Urbach energy is compared with the absorption edge energy derived from density functional theory (DFT) calculation. For this purpose, the absorption spectra of solar cell materials, including CdTe, CuInSe2 (CISe), CuGaSe2 (CGSe), Cu2ZnSnSe4 (CZTSe), Cu2ZnSnS4 (CZTS) and hybrid perovskites, have been calculated by DFT particularly using very-high-density k meshes. As a result, we find that the tail state formation is negligible in CdTe, CISe, CGSe and hybrid perovskite polycrystals. However, coevaporated CZTSe and CZTS layers exhibit very large Urbach energies, which are far larger than the theoretical counterparts. Based on DFT analysis results, we conclude that the quite large tail state formation observed in the CZTSe and CZTS originates from extensive cation disordering. In particular, even a slight cation substitution is found to generate unusual band fluctuation in CZT(S)Se. In contrast, CH3NH3PbI3 hybrid perovskite shows the sharpest absorption edge theoretically, which agrees with experiment.

Electronic Properties of Incommensurate Atomic Layers

We present a brief theoretical overview of electronic properties of incommensurate multilayer systems, i.e., a pair of two-dimensional atomic layers stacked in an arbitrary orientation. We introduce the general theoretical scheme to describe the interlayer interaction between incommensurate crystal structures, and apply the formula to two specific examples, the twisted bilayer graphene and graphene–hBN composite bilayer. In each case, we calculate the electronic band structure and demonstrate that the low-energy electronic properties are significantly modified by the interlayer interaction, particularly when the two lattice structures are close to each other. We also study the energy spectrum and the quantum Hall effect in magnetic fields, where we see that the spectral structure exhibits a fractal nature, as known as the Hofstadter butterfly. We argue about the optical absorption properties of the twisted bilayer graphene and show that the interlayer interaction gives rise to the characteristic spectrosc...

Computational Study of the Decomposition of Cyclotetramethylenetetranitramine under Impact, Friction, and Electric Fields

Organic CHNO-containing high energy density materials have been widely used for storing large amounts of the chemical energies which can be rapidly transformed into heat upon various external perturbations during detonation. The sensitivity of the energetic materials is subjected to considerable concern for safety and maintenance. Periodic density functional theory with the all-electron basis sets were employed in this work to unravel the impact, friction, and electric-fields induced decomposition of HMX. The minimum energy paths for the N−NO2homolysis reactions of HMX in the bulk and gas phases were obtained. The surface-enhanced effect on the decomposition of HMX were calculated for both (010) and (100) surfaces. A general theoretical scheme has been proposed to assess the intrinsic mechanic and electrostatic sensitivities of the pure energetic materials.

Crossover from electromagnetically induced transparency to Autler–Townes splitting in open ladder systems with Doppler broadening

We propose a general theoretical scheme to investigate the crossover from electromagnetically induced transparency (EIT) to Autler-Townes splitting (ATS) in open ladder-type atomic and molecular systems with Doppler broadening. We show that when the wavenumber ratio $k_c/k_p\approx -1$, EIT, ATS, and EIT-ATS crossover exist for both ladder-I and ladder-II systems, where $k_c$ ($k_p$) is the wavenumber of control (probe) field. Furthermore, when $k_c/k_p$ is far from $-1$ EIT can occur but ATS is destroyed if the upper state of the ladder-I system is a Rydberg state. In addition, ATS exists but EIT is not possible if the control field used to couple the two lower states of the ladder-II system is a microwave field. The theoretical scheme developed here can be applied to atoms, molecules, and other systems (including Na$_2$ molecules, and Rydberg atoms), and the results obtained may have practical applications in optical information processing and transformation.

Equifinality and its violations in a redundant system: multifinger accurate force production

We explored a hypothesis that transient perturbations applied to a redundant system result in equifinality in the space of task-related performance variables but not in the space of elemental variables. The subjects pressed with four fingers and produced an accurate constant total force level. The "inverse piano" device was used to lift and lower one of the fingers smoothly. The subjects were instructed "not to intervene voluntarily" with possible force changes. Analysis was performed in spaces of finger forces and finger modes (hypothetical neural commands to fingers) as elemental variables. Lifting a finger led to an increase in its force and a decrease in the forces of the other three fingers; the total force increased. Lowering the finger back led to a drop in the force of the perturbed finger. At the final state, the sum of the variances of finger forces/modes computed across repetitive trials was significantly higher than the variance of the total force/mode. Most variance of the individual finger force/mode changes between the preperturbation and postperturbation states was compatible with constant total force. We conclude that a transient perturbation applied to a redundant system leads to relatively small variance in the task-related performance variable (equifinality), whereas in the space of elemental variables much more variance occurs that does not lead to total force changes. We interpret the results within a general theoretical scheme that incorporates the ideas of hierarchically organized control, control with referent configurations, synergic control, and the uncontrolled manifold hypothesis.

Organizational requirements for multicellular autonomy: insights from a comparative case study

In this paper we explore the organizational conditions underlying the emergence of organisms at the multicellular level. More specifically, we shall propose a general theoretical scheme according to which a multicellular organism is an ensemble of cells that effectively regulates its own development through collective (meta-cellular) mechanisms of control of cell differentiation and cell division processes. This theoretical result derives from the detailed study of the ontogenetic development of three multicellular systems (Nostoc punctiforme, Volvox carteri and Strongylocentrotus purpuratus) and, in particular, of their corresponding cell-to-cell signaling networks. The case study supports our claim that a specific type of functional integration among the cells of a multicellular ensemble (namely, a regulatory control system consisting in several inter-cellular mechanisms that modulate epigenesis and whose operation gets decoupled from the intra-cellular metabolic machinery), is required for it to qualify as a proper organism. Finally, we argue why a multicellular system exhibiting this type of functionally differentiated and integrated developmental organization becomes a self-determining collective entity and, therefore, should be considered as a second-order autonomous system.

Analysis of vacuum ultraviolet electronic spectra of Ce3+ and Pr3+ ions in Ca9Lu(PO4)7: crystal-field calculations and simulation of optical spectra

The 4f–5d excitation and emission spectra of Ce3+ and Pr3+ ions in Ca9Lu(PO4)7 as recently reported (2012 J. Phys.: Condens. Matter 24 385502) were further analyzed and simulated by employing the effective Hamiltonian model for the 4fN and 4fN−15d electronic configurations of impurity lanthanide ions and the exchange charge model of crystal-field theory. The multi-site effect on the 4f–5d transition spectra was explicitly discussed from the points of view of the local structure and site occupation ratios of lanthanide ions in Ca9Lu(PO4)7. An excellent agreement between the predicted and measured spectra confirms the validity of the performed calculations. Based on these energy level and intensity calculation results, the radiative lifetimes of the 5d–4f emissions of Ce3+ and Pr3+ ions have been modeled to show nearly independent temperature trends. Comparison with the measured lifetimes suggests the nonradiative relaxation process in this host is probably related to the intrinsic defect states. In addition to the studies of the 4f–5d transitions, a general theoretical scheme to calculate the lowest 4f–6s transition energy of the Ce3+ ion was proposed for the first time on the basis of the ligand polarization model. The predicted 6s energy position of the Ce3+ ion in Ca9Lu(PO4)7 is solid evidence corroborating our previous spectroscopic assignment.

Arbitrary violation of the Tsirelson bound

We present a simple hidden variable model for the singlet state of a pair of qubits, characterized by two kinds, hierarchically ordered, of hidden variables. We prove that, averaging over both types of variables, one reproduces all the quantum mechanical correlations of the singlet state. On the other hand, averaging only over the hidden variables of the lower level, one obtains a general formal theoretical scheme exhibiting correlations stronger than the quantum ones, but with faster-than-light communication forbidden. This result is interesting by itself since it shows that a violation of the quantum bound for nonlocal correlations can be implemented in a precise physical manner and not only mathematically, and it suggests that resorting to two levels of nonlocal hidden variables might led to a deeper understanding of the physical principles at the basis of quantum nonlocality.

Thermal stresses in a coating layer. I. General theoretical scheme

The evolution of thermal stresses generated by a thermal perturbation of cylindrical symmetry in a flat infinite isotropic thermoelastic layer of constant (before perturbation) thickness on a half-space rigid substrate is theoretically investigated. The problem is considered in the framework of uncoupled linear thermoelasticity, in the quasi-stationary displacement field approximation. Thermal insulation of the layer is considered in two versions: (a) both its surfaces are adiabatically insulated, and (b) the free surface is adiabatically insulated, whereas the contact surface is kept at constant temperature. The free surface of the layer is assumed to be stress free, and the contact surface is kept on a rigid substrate. The proper equations are solved using suitable Hankel and Fourier transformations. Part I of the paper presents a general theoretical scheme of the problem in a general case (without specification of the perturbation), and it is illustrated by a simple, detailed example (time evolution of stresses at the contact surface of the layer, generated by a surface point instantaneous heat pulse in case a). The analysis of stresses in more realistic cases, modeling realistic situations will be presented in Part II.

Prior model evaluation from Null Space Compensation perspective with application to surface reconstruction from single images

Prior model is widely applied in the area of computer vision and computer graphics. However, there is still a lack of a general theoretical scheme for evaluating the performance of the priors and a guidance for choosing suitable models. In this paper, a general scheme is proposed for linear singular problems based on the idea of Null Space Compensation. It is proved that for a linear prior model the principal directions obtained from the singular value decomposition of the model shall not be parallel to those of the system matrix determined by the problem. It is also suggested that for a nonlinear prior, higher correlation between the null space components of the estimate data based on the given prior and those of the ground truth or controlled data indicate the better suitability of the prior. The proposed evaluation scheme is demonstrated through an application to a linearized shape from shading problem, where surface shall be reconstructed from single 2D images. Both linear model and nonlinear constraints are evaluated with experiments on both synthetic images and real images. The results validate the proposed evaluation scheme and its capability for guiding in choosing a good prior model structure.