Infinitesimal Field Research Articles

Characterization of dual curves using the theory of infinitesimal bending

In this paper, we generalize the main ideas and statements of the theory of infinitesimal bending in Euclidean 3‐space to dual curves in the dual 3‐space . The basic condition we introduce is the invariance of the dual arc length with appropriate precision. Necessary and sufficient conditions for the dual field to be an infinitesimal bending field are given. Some useful formulas and facts about dual arc length and dual bending field are obtained. An explicit characterization of the dual spherical curve bending is presented, and the corresponding infinitesimal bending field is decomposed into dual vectors of the dual Frenet frame. Finally, some examples are given to illustrate our results.

Long-range interacting Stark many-body probes with super-Heisenberg precision

In contrast to interferometry-based quantum sensing, where interparticle interaction is detrimental, quantum many-body probes exploit such interactions to achieve quantum-enhanced sensitivity. In most of the studied quantum many-body probes, the interaction is considered to be short-ranged. Here, we investigate the impact of long-range interaction at various filling factors on the performance of Stark quantum probes for measuring a small gradient field. These probes harness the ground state Stark localization phase transition which happens at an infinitesimal gradient field as the system size increases. Our results show that while super-Heisenberg precision is always achievable in all ranges of interaction, the long-range interacting Stark probe reveals two distinct behaviors. First, by algebraically increasing the range of interaction, the localization power is enhanced and thus the sensitivity of the probe decreases. Second, as the interaction range becomes close to a fully connected graph its effective localization power disappears and thus the sensitivity of the probe starts to enhance again. The super-Heisenberg precision is achievable throughout the extended phase until the transition point and remains valid even when the state preparation time is incorporated in the resource analysis. As the probe enters the localized phase, the sensitivity decreases and its performance becomes size-independent, following a universal behavior. In addition, our analysis shows that lower filling factors lead to better precision for measuring weak gradient fields.

Giant magnetoelectricity in soft materials using hard magnetic soft materials

Imagine a material that will produce electricity via a contactless, wireless signal. Further, we hope that this material is capable of large deformation reminiscent of soft robots and is soft enough to conform to irregular or curved geometries. This would all be possible if soft magnetoelectric materials were available; paving the way for applications such as remote drug delivery, energy harvesting, soft robots, multiple state memories among others. Here, for the first time, using the concept of hard magnetic soft matter in combination with electrets, we design and create a soft magnetoelectric material that exhibits an extremely strong, self-biased magnetoelectric effect. Further, using programmable pattern of deposition of magnetic dipoles and charges, we report a giant magnetoelectric coefficient in an ultra-soft deformable material that retains its strength even under infinitesimal external fields and at low frequencies.

Surfaces defined by bending of knots

We consider the definition of the infinitesimal bending of a curve as a vector parametric equation of a surface defined by two free variables: one of them is free variable u which define curve and another is bending parameter ?. In this way, while being bent curve is deformed and moved through the space forming a surface. If infinitesimal bending field is of constant intensity, deformed curves form a ruled surface that represents a ribbon. In particular, we consider surfaces obtain by bending of knots both analytically and graphically. We pay attention to the torus knot and possibility of its infinitesimal bending so that the surface determined by bending is a part of the initial torus.

Implementation of real‐time TDDFT for periodic systems in the open‐source PySCF software package

We present a new implementation of real-time time-dependent density functional theory (RT-TDDFT) for calculating excited-state dynamics of periodic systems in the open-source Python-based PySCF software package. Our implementation uses Gaussian basis functions in a velocity gauge formalism and can be applied to periodic surfaces, condensed-phase, and molecular systems. As representative benchmark applications, we present optical absorption calculations of various molecular and bulk systems and a real-time simulation of field-induced dynamics of a (ZnO)4 molecular cluster on a periodic graphene sheet. We present representative calculations on optical response of solids to infinitesimal external fields as well as real-time charge-transfer dynamics induced by strong pulsed laser fields. Due to the widespread use of the Python language, our RT-TDDFT implementation can be easily modified and provides a new capability in the PySCF code for real-time excited-state calculations of chemical and material systems.

Infinitesimal bending of DNA helices

The mathematics of DNA molecules is often studied as a double helix model. This paper focuses on the modelling of infinitesimal bending of DNA helices. The paper checks the flexibility of DNA molecule, i.e. the flexibility of double helix in infinitesimal bending theory. Actually, first, we find infinitesimal bending field of an arbitrary curve on the helicoid, that leaves bent curves on the helicoid, and show that helix bending on the helicoid is not possible. Finally, we deal with the infinitesimal bending of helicoid, using PDEs. Visualization of infinitesimal bending was done in Mathematica.

Large-Scale Shape Transformations of a Sphere Made of a Magnetoactive Elastomer.

Magnetostriction effect, i.e., deformation under the action of a uniform applied field, is analyzed to detail for a spherical sample of a magnetoactive elastomer (MAE). A close analogy with the field-induced elongation of spherical ferrofluid droplets implies that similar characteristic effects viz. hysteresis stretching and transfiguration into a distinctively nonellipsoidal bodies, should be inherent to MAE objects as well. The absence until now of such studies seems to be due to very unfavorable conclusions which follow from the theoretical estimates, all of which are based on the assumption that a deformed sphere always retains the geometry of ellipsoid of revolution just changing its aspect ratio under field. Building up an adequate numerical modelling tool, we show that the ‘ellipsoidal’ approximation is misleading beginning right from the case of infinitesimal field strengths and strain increments. The results obtained show that the above-mentioned magnetodeformational effect should distinctively manifest itself in the objects made of quite ordinary MAEs, e.g., composites on the base of silicone cautchouc filled with micron-size carbonyl iron powder.

Strain Pattern and Kinematics of the Canary Islands from GNSS Time Series Analysis

Following the 2004 seismic unrest at Tenerife and the 2011–2012 submarine eruption at El Hierro, the number of Global Navigation Satellite System (GNSS) observation sites in the Canary Islands (Spain) has increased, offering scientists a useful tool with which to infer the kinematics and present-day surface deformation of the Canary sector of the Atlantic Ocean. We take advantage of the common-mode component filtering technique to improve the signal-to-noise ratio of the velocities retrieved from the daily solutions of 18 permanent GNSS stations distributed in the Canaries. The analysis of GNSS time series spanning the period 2011–2017 enabled us to characterize major regions of deformation along the archipelago through the mapping of the 2D infinitesimal strain field. By applying the triangular segmentation approach to GNSS velocities, we unveil a variable kinematic behaviour within the islands. The retrieved extension pattern shows areas of maximum deformation west of Tenerife, Gran Canaria and Fuerteventura. For the submarine main seismogenic fault between Tenerife and Gran Canaria, we simulated the horizontal deformation and strain due to one of the strongest (mbLg 5.2) earthquakes of the region. The seismic areas between islands, mainly offshore Tenerife and Gran Canaria, seem mainly influenced by the regional tectonic stress, not the local volcanic activity. In addition, the analysis of the maximum shear strain confirms that the regional stress field influences the E–W and NE–SW tectonic lineaments, which, in accordance with the extensional and compressional tectonic regimes identified, might favour episodes of volcanism in the Canary Islands.

Hadamard’s conditions of compatibility from Cesaro’s line-integral representation

A given symmetric and compatible linear transformation field D determines, through Cesaro representation theorem, a vector field v whose symmetric gradient ∇sv equals D, up to an additive vector field vh satisfying ∇svh=0. If D represents an infinitesimal strain field, then vh is an infinitesimal rigid-body displacement. If D represents a stretching field, then vh is a rigid-body velocity which characterizes a rate of translation and rotation of the whole (fluid or solid) body.If D is compatible in regions separated by a smooth singular surface across which D suffers a jump, then in our main Theorem 2.3 we show that the associated vector field v must satisfy the Hadamard rank 1 compatibility condition across the surface, i.e., the jump ⟦∇v⟧ is rank 1 of the form d⊗n, where n is a unit normal to the surface, if and only if ⟦∇v⟧ is constant across the singular surface. Importantly, no a priori stated restriction on the skewsymmetric part of ∇v is needed. We, then, record two corollaries that characterize the possible jump behavior at a corner line where two smooth singular surfaces meet, discussing how our results apply in two example elementary flow problems in classical fluid dynamics.

Electric-field-induced Z2 topological phase transition in strained single bilayer Bi(111)

For controlling critical electric fields of the topological phase transition in a single bilayer Bi(111), we investigated topological phases in a strained system through first-principles calculations. We found a quadratic band touching semimetallic state at tensile strain ϵ = 0.5%. Around this strain, the topological phase can be switched to a trivial insulator by an infinitesimal electric field. The momentum positions at which Dirac cones appear in the electric-field-induced topological phase transition changed for the strain ϵ > 0.5% and ϵ < 0.5%. Our results indicate that this topological phase transition could be applied to novel spintronic devices.

3D crystallographic alignment of alumina ceramics by application of low magnetic fields

Non-cubic crystals exhibit anisotropic physical and functional properties. Microscopic crystallites as constituents of polycrystalline materials are randomly oriented, thus polycrystalline ceramics lack the anisotropic properties of their monocrystalline counterparts. We propose a technology that exploits the synergy between magnetic alignment and colloidal ceramics processing, and enables to independently tune the orientation of grains in different sample regions by infinitesimal magnetic fields (<10 mT). The grain pivot mechanism enables the emulation of single crystals, as well as the creation of large complex-shaped ceramic elements with designed crystallographic landscapes and spatially and directionally tuned properties. Ultra-high magnetic response arises from magnetic shape anisotropy of platelet-shaped seed crystallites coated with small amounts of iron oxide nanoparticles. To control crystallographic growth directions during subsequent annealing procedures, the seeds are dispersed and aligned in a matrix of chemically identical, but much finer spherical particles. This technology opens an avenue to remarkably improve structural and functional properties of ceramic elements employed in numerous industrial applications.

Random-field-induced disordering mechanism in a disordered ferromagnet: Between the Imry-Ma and the standard disordering mechanism

Random fields disorder Ising ferromagnets by aligning single spins in the direction of the random field in three space dimensions, or by flipping large ferromagnetic domains at dimensions two and below. While the former requires random fields of typical magnitude similar to the interaction strength, the latter Imry-Ma mechanism only requires infinitesimal random fields. Recently, it has been shown that for dilute anisotropic dipolar systems a third mechanism exists, where the ferromagnetic phase is disordered by finite-size glassy domains at a random field of finite magnitude that is considerably smaller than the typical interaction strength. Using large-scale Monte Carlo simulations and zero-temperature numerical approaches, we show that this mechanism applies to disordered ferromagnets with competing short-range ferromagnetic and antiferromagnetic interactions, suggesting its generality in ferromagnetic systems with competing interactions and an underlying spin-glass phase. A finite-size-scaling analysis of the magnetization distribution suggests that the transition might be first order.

Field-Induced Instability of a Gapless Spin Liquid with a Spinon Fermi Surface.

The ground state of the quantum kagome antiferromagnet Zn-brochantite, ZnCu_{3}(OH)_{6}SO_{4}, which is one of only a few known spin-liquid (SL) realizations in two or three dimensions, has been described as a gapless SL with a spinon Fermi surface. Employing nuclear magnetic resonance in a broad magnetic-field range down to millikelvin temperatures, we show that in applied magnetic fields this enigmatic state is intrinsically unstable against a SL with a full or a partial gap. A similar instability of the gapless Fermi-surface SL was previously encountered in an organic triangular-lattice antiferromagnet, suggesting a common destabilization mechanism that most likely arises from spinon pairing. A salient property of this instability is that an infinitesimal field suffices to induce it, as predicted theoretically for some other types of gapless SLs.

Open string T-duality in a weakly curved background

We consider a theory of an open string moving in a weakly curved background, composed of a constant metric and a linearly coordinate dependent Kalb-Ramond field with an infinitesimal field strength. We find its T-dual using the generalized Buscher procedure developed for the closed string moving in a weakly curved background, and the fact that solving the boundary conditions, the open string theory transforms to the effective closed string theory. So, T-dualizing the effective theory along all effective directions we obtain its T-dual theory and resume the open sting theory which has such an effective theory. In this way we obtain the open string theory T-dual.

Infinitesimal bending influence on the Willmore energy of curves

In this paper we study the change of the Willmore energy of curves, as a special case of so-called Helfrich energy, under infinitesimal bending determined by the stationarity of arc length. We examine the variation of the unit tangent, principal normal and binormal vector fields, the curvature and the torsion of the curve. We obtain an explicit formula for calculating the variation of the Willmore energy, as well as the Euler-Lagrange equations describing equilibrium. We find an infinitesimal bending field for a helix and compute the variation of its Willmore energy under such infinitesimal bending.

Symmetry analysis of reaction diffusion equation with distributed delay

This paper study the reaction–diffusion equation with distributed delay from the Lie group theoretic point of view. We give at first the evolutionary infinitesimal vector field v and a number of group invariant solutions corresponding to v by general symmetry group theory.

Quantum disorder and local modes of the fully-frustrated transverse field Ising model on a diamond chain

We investigate the transverse field Ising model on a diamond chain using series expansions about the high-field limit and exact diagonalizations. For the unfrustrated case we accurately determine the quantum critical point and its expected 2d Ising universality separating the polarized and the Z2 symmetry broken phase. In contrast, we find strong evidences for a disorder by disorder scenario for the fully-frustrated transverse field Ising model, i.e. except for the pure Ising model, having an extensive number of ground states, the system is always in a quantum disordered polarized phase. The low-energy excitations in this polarized phase are understood in terms of exact local modes of the model. Furthermore, an effective low-energy description for an infinitesimal transverse field allows to pinpoint the quantum disordered nature of the ground state via mapping to an effective transverse field Ising chain and to determine the induced gap to the elementary effective domain wall excitation very accurately.

Quantum phase transition in a disordered long-range transverse Ising antiferromagnet

We consider a long-range Ising antiferromagnet put in a transverse field (LRTIAF) with disorder. We have obtained the phase diagrams for both the classical and quantum cases. For the pure case applying quantum Monte Carlo method, we study the variation in order parameter (spin correlation in the Trotter direction), susceptibility, and average energy of the system for various values of the transverse field at different temperatures. The antiferromagnetic order is seen to get immediately broken as soon as the thermal or quantum fluctuations are added. We discuss generally the phase diagram for the same LRTIAF model with perturbative Sherrington-Kirkpatrick-type disorder. We find that while the antiferromagnetic order is immediately broken as one adds an infinitesimal transverse field or thermal fluctuation to the pure LRTIAF system, an infinitesimal SK spin-glass disorder is enough to induce a stable glass order in the LRTIAF. This glass order eventually gets destroyed as the thermal or quantum fluctuations are increased beyond their threshold values and the transition to paramagnetic phase occurs. Analytical studies for the phase transitions are discussed in details in each case. These transitions have been confirmed by applying classical and quantum Monte Carlo methods. We show here that the disordered LRTIAF has a surrogate incubation property of the SK spin glass phase.

Curvebend graphical tool for presentation of infinitesimal bending of curves

An infinitesimal bending of the curve at E3 is considered and the infinitesimal bending field is determined and discussed. CurveBend, tool for graphical presentation of non rigid curves is presented. Influence of infinitesimal bending field on curves is discussed and visualized by the tool.

A novel quantum transition in a fully frustrated transverse Ising antiferromagnet

We consider a long-range Ising antiferromagnet (LRIAF) put in a transverse field. Applying quantum Monte Carlo method, we study the variation of order parameter (spin correlation in Trotter time direction), susceptibility and average energy of the system for various values of the transverse field at different temperatures. The antiferromagnetic order is seen to get immediately broken as soon as the thermal or quantum fluctuations are added. We also discuss the phase diagram for the Sherrington-Kirkpatrick (SK) model with the same LRIAF bias, also in presence of a transverse field. We find that while the antiferromagnetic order is immediately broken as one adds an infinitesimal transverse field or thermal fluctuation to the system, an infinitesimal SK spin glass disorder is enough to induce a stable glass order in the antiferromagnet. This glass order eventually gets destroyed as the thermal or quantum fluctuations increased beyond their threshold values and the transition to para phase occurs. Indications of this novel phase transition are discussed. Because of the presence of full frustration, this surrogate property of the LRIAF for incubation of stable spin glass phase in it (induced by addition of a small disorder) should enable eventually the study of classical and quantum spin glass phases by using some perturbation theory with respect to the disorder.