Exact Compatibility Research Articles

Semiclassical gravitational collapse of a radially symmetric massless scalar quantum field

We present a method to study the semiclassical gravitational collapse of a radially symmetric scalar quantum field in a coherent initial state. The formalism utilizes a Fock space basis in the initial metric, is unitary and time reversal invariant up to numerical precision. It maintains exact compatibility of the metric with the expectation values of the energy momentum tensor in the scalar field coherent state throughout the entire time evolution. We find a simple criterion for the smallness of discretization effects, which is violated when a horizon forms. As a first example, we study the collapse of a specific state in the angular momentum $l=0$ approximation. Outside the simulated volume it produces a Schwarzschild metric with $r_s \sim 3.5 \ell_p$. We see behaviour that is compatible with the onset of horizon formation both in the semiclassical and corresponding classical cases in a regime where we see no evidence for large discretization artefacts. In our example setting, we see that quantum effects accelerate the possible horizon formation and move it radially outward. We find that this effect is robust against variations of the radial resolution, the time step, the volume, the initial position and shape of the inmoving state, the vacuum subtraction, the discretization of the time evolution operator and the integration scheme of the metric. We briefly discuss potential improvements of the method and the possibility of applying it to black hole evaporation. We also briefly touch on the extension of our formalism to higher angular momenta, but leave the details and numerics for a forthcoming publication.

Insights from exact exchange-correlation kernels

The exact exchange-correlation (xc) kernel ${f}_{\text{xc}}(x,{x}^{\ensuremath{'}},\ensuremath{\omega})$ of linear response time-dependent density functional theory is computed over a wide range of frequencies for three canonical one-dimensional finite systems. Methods used to ensure the numerical robustness of ${f}_{\text{xc}}$ are set out. The frequency dependence of ${f}_{\text{xc}}$ is found to be largely due to its analytic structure, i.e., its singularities at certain frequencies, which are required in order to capture particular transitions, including those of double excitation character. However, within the frequency range of the first few interacting excitations, ${f}_{\text{xc}}$ is approximately $\ensuremath{\omega}$ independent, meaning the exact adiabatic approximation ${f}_{\text{xc}}(\ensuremath{\omega}=0)$ remedies the failings of the local density approximation and random phase approximation for these lowest transitions. The key differences between the exact ${f}_{\text{xc}}$ and its common approximations are analyzed, and cannot be eliminated by exploiting the limited gauge freedom in ${f}_{\text{xc}}$. The optical spectrum benefits from using as accurate as possible an ${f}_{\text{xc}}$ and ground-state xc potential, while maintaining exact compatibility between the two is of less importance.

Superior MoS2-decorated CNT composite materials for photoelectric detectors

Carbon nanotubes (CNTs), outstanding flexible and photoelectric materials, have inspired tremendous innovations in the fields of stretchable and wearable electronics. Exquisite optoelectronic materials are decorated on carbon nanotube walls is an universal method under modification process for CNT. This modification promotes the light-matter interactions and efficient charge-transfer pathways. In this respect, it is still challenging to prepare excellent CNT composites and fabricate state-of-the-art carbon-based flexible electronic devices effectly. Herein, we designed a MoS2-decorated CNT photoelectric composite materials by a facile self-assembly method, which realized exact compatibility and ingenious connection of CNT and MoS2. The flexible photoelectric electronic devices were fabricated by micro-nanofabrication technologies. The photocurrent of CNT-MoS2 exhibited 4 times higher than pure CNT materials, which showed superior photoresponse and recovery ability. The photoinduced charge transfer theory proved that the MoS2 is exceedingly good optical gain materials and benefiting from the interfacial charge-transfer transition. Therefore, the MoS2 can serve as a complement in applications that require excellent photovoltaic semiconductors, which has potential for obstaining the novel proporties nanomaterial system. The enhancement of photosensing performance showing the broad prospect of the burgeoning high performance wearable sensors.

Genetic Diversity of Oilseed Rape Fields and Feral Populations in the Context of Coexistence with GM Crops.

Despite growing concern about transgenes escaping from fields, few studies have analysed the genetic diversity of crops in an agroecosystem over several years. Accurate information about the dynamics and relationship of the genetic diversity of crops in an agroecosystem is essential for risk assessment and policies concerning the containment of genetically modified crops and their coexistence with crops grown by conventional practices. Here, we analysed the genetic diversity of oilseed rape plants from fields and feral populations over 4 years in an agricultural landscape of 41 km2. We used exact compatibility and maximum likelihood assignment methods to assign these plants to cultivars. Even pure lines and hybrid cultivar seed lots contained several genotypes. The cultivar diversity in fields reflected the conventional view of agroecosystems quite well: that is, there was a succession of cultivars, some grown for longer than others because of their good performance, some used for one year and then abandoned, and others gradually adopted. Three types of field emerged: fields sown with a single cultivar, fields sown with two cultivars, and unassigned fields (too many cultivars or unassigned plants to reliably assign the field). Field plant diversity was higher than expected, indicating the persistence of cultivars that were grown for only one year. The cultivar composition of feral populations was similar to that of field plants, with an increasing number of cultivars each year. By using genetic tools, we found a link between the cultivars of field plants in a particular year and the cultivars of feral population plants in the following year. Feral populations on road verges were more diverse than those on path verges. All of these findings are discussed in terms of their consequences in the context of coexistence with genetically modified crops.

Decay Estimates for Elastic Cylinders with Mixed Boundary Conditions

The classical Saint-Venant’s problem in cylinders is considered under various boundary conditions and some estimates are proven. In particular, if the cylinder is force free on the mantle and is subject to assigned displacements on the bases, satisfying exact compatibility conditions, then a unique elementary Saint-Venant’s solution can be selected in such a way that it agrees with the rigorous solution to the mixed problem away from the bases.

A multi-purpose reflective fiber optic sensor

Fiber optic sensors, including reflective ones, have widespread applications in sensing technology. In this study, we first formulated the gain of a general reflective fiber optic sensor in terms of five major sensor parameters, and for two patterns of input intensity: namely uniform and Gaussian. By using these formulae, we have analyzed and plotted the variations of gain versus one or two of these parameters. The results obtained have exact compatibility for the two patterns of input intensity, although they have been obtained by different methods. The results can be suitably used in the optimum design of a wide variety of reflective fiber optic sensors.

A sharp interface model of compatible twin patterns in shape memory alloys

The cubic–orthorhombic shape memory alloy system is studied using a sharp interface model based on the linear theory of compatible laminates. A computational method is developed to generate all possible compatible laminates for a given state of strain, and check whether these laminates satisfy exact compatibility conditions. The type of austenite–martensite interface that can form is dependent upon the detail of the martensite structure; the formation of flat and wedge-like austenite–martensite interfaces is explored. A full search is used to reveal the routes in strain space along which the two-phase structure can continuously evolve. A variety of laminate structures, some well known and some new, are reported. The methods developed are readily applied to other crystal systems, such as the tetragonal crystal system, in shape memory alloys or related materials.

Classification of laminate domain patterns in ferroelectrics

Ferroelectric crystals are known to adopt low-energy, compatible domain configurations. Observations show that these configurations are commonly multirank laminate patterns. In this work, a method to classify and enumerate the laminate domain patterns that can form is presented. The criteria of exact compatibility for laminates structures in a ferroelectric single crystal are used to find all the rank-2 arrangements of domains in the polar tetragonal crystal system. Surprisingly, only eight distinct rank-2 laminate patterns that satisfy compatibility conditions at all domain walls are found. These patterns are classified and correlated with observations of domains in single crystals, showing good agreement.

Compatible domain structures and the poling of single crystal ferroelectrics

Ferroelectric crystals are known to adopt low energy, compatible configurations of microstructure. Many models have been proposed to describe these low-energy domain configurations, mainly based on the idea of fine phase mixtures and average compatibility. The present work develops criteria for the exact compatibility of domain structure in the form of a periodic multi-rank laminate. Exactly compatible structure is expected to be energetically favourable and does not require the concept of a fine mixture. A hierarchical binary tree representation is used to describe the relations among the domains in a multi-rank laminate, and this enables a concise statement of the conditions for exact compatibility. The disclinations associated with domain junctions are also taken into account. The resulting method is a rapid and systematic procedure for finding exactly compatible domain arrangements. This is used to explore minimum rank compatible microstructure in the tetragonal and rhombohedral crystal systems. The results reveal routes in polarization and strain space along which the microstructure can continuously evolve, including low-rank poling paths for single crystals. The method generates several well known domain configurations and many new structures.

Compatible domain arrangements and poling ability in oriented ferroelectric films

The microstructure in single crystal ferroelectric films is significantly affected by the substrate conditions and the crystallographic orientation of the film. Domain arrangements form to minimize the total energy producing a stable state corresponding to the external boundary conditions. In order to find low energy domain arrangements, this study uses exact compatibility conditions for periodic laminate structures which ensure that all the adjacent domains fit together compatibly. These conditions are applied to films with various orientations and crystal systems, such as the rhombohedral and tetragonal crystal systems. A systematic search is used to discover exactly compatible structures for given states of macroscopic strain and polarization in the film. The theory is applied to [001], [011], and [111] oriented rhombohedral and tetragonal films. The results indicate poling paths along which the microstructure can evolve continuously while maintaining compatibility, to get from a state of zero through-thickness polarization to the state with the greatest value of through-thickness polarization. The evolution of the domain arrangement along these poling paths is shown, and the poling ability, or the limit on the maximum polarization achieved, is discussed. The influence of a strain state imposed by the substrate on the microstructure and poling ability is studied. The use of the model is illustrated by developing poling maps for a tetragonal [001] oriented film to show the set of polarization states that can be achieved as a function of the imposed substrate strain.

Surface deformations and domains in Terfenol-D by scanning probe microscopy

This paper reports the first direct measurements of the deformations in the surface of a ferromagnet caused by magnetostrictive lattice strains in neighboring magnetic domains. Observations of the {011} and {112} surfaces of twinned Terfenol-D (Tb0.3Dy0.7Fe2) crystals by atomic force microscopy reveal the deformation domains previously imaged by optical microscopy and predicted by recent theory. The surface topography has been imaged in the remanent and ac demagnetized states and measurements of the deformation gradients have enabled the magnetostriction constant in the 〈111〉 direction to be estimated as 1.63×10−3 to within 8%. All theoretically predicted deformation domains have been observed and, in particular, the exact compatibility of such deformations across the growth twin boundaries is clearly revealed. The magnetic domains associated with the observed deformations are inferred from magnetic force microscopy observations which yield complex contrast patterns.

Component mode iteration for frequency calculations

This paper presents mode iteration, a new method for carrying out a form of subspace iteration on the substructure level, for structures composed of substructures. In mode iteration, substructure displacement is in terms of component with the interface displacements as coefficients. Component modes are chosen such that exact compatibility is assured throughout the structure. The reduced structure eigenvalue problem is assembled and solved for lower mode approximations. The resulting estimates of lower mode interface motion are used to refine the modes by approximating the dynamic response of substructures to interface motion with a vector iteration process. For this step, the substructures are independent and can be processed in parallel. Reassembly and solution of the reduced structure problem yields improved lower mode estimates. Further iterations of refinement and reassembly are performed until convergence takes place. The initial modes are generated automatically and at negligible expense and numerical examples show that convergence with these is excellent, yielding very accurate results after only one iteration. Indeed, convergence is shown to be significantly faster than in the standard subspace iteration method.

Finite element criteria for some shells

AbstractSimple solutions are extracted from the exact compatibility equations of inextensional bending for a special class of shell shapes, and it is speculated that these solutions provide useful criteria towards evaluating finite elements for these and closely related shapes. Curved finite elements of a quadratic parametric representation, which do not belong to the special class, are then studied. By using a series of exact inextensional bending displacements, it is concluded from numerical evidence that the criteria apply to finite element shapes in this representation when they are shallow, as is usually the case in practice. Criteria for homogeneous membrane actions follow from Gol'denveizer's static–geometric analogue.

Behaviour at x = 0, 1, sum rules and parametrizations for structure functions beyond the leading order

We write the simplest possible parametrizations of deep inelastic structure functions which satisfy the following requirements: (i) exact compatibility with QCD at the endpoints x =0, 1, to second order; (ii) fulfilment of sum rules to second order; (iii) leading and subleading Regge behaviour. In all we find that, including the QCD scale Λ, such parametrizations describe in a simple manner the three standard functions W 1, W 2, W 3 for all x, Q 2 in terms of four to six parameters only (two more if allowing for higher twists).