Geometric Decoupling Research Articles

Relativistic fluids interacting through gravitational decoupling in f(T,𝒯) theory

In this paper, we will manifest how polytropic fluids produce effects on an alternate gravitational source, regardless of its features, for spherically symmetric and static spacetimes. For this purpose, we use [Formula: see text] modified gravity, which is characterized by the trace of an energy–momentum tensor as [Formula: see text] and torsion scalar [Formula: see text], Additionally, using the polytropic equation of state, we will speculate about the distribution of energy among fluids within an astrophysical object. We offer a thorough methodology for identifying generic relativistic polytropes accompanied by the minimal geometric decoupling technique. Ultimately, a few tangible attributes of polytropes along with perfect fluids are observed using the Tolman IV solution, including total pressure, energy interchange, and thermal characteristics.

Compact stars with dark matter induced anisotropy in complexity-free background and effect of dark matter on GW echoes

ABSTRACT In this work, we consider the vanishing complexity factor scenario which has opened up a whole new way of generating solutions to the Einstein field equations for the spherically symmetric structure of celestial bodies. By using this very rare condition on the system of two metric potentials, viz. gtt and grr, we make reduce it to a uni-metric potential system satisfying all physical conditions. Along with this, we further have considered that the space–time is deformed by dark matter (DM) content in DM haloes resulting into perturbations in the gtt and grr metric potentials. This DM deformation is mathematically done by the complete geometric decoupling method where the decoupling parameter β decides the amount of DM content. In connection to the claimed post-merger object in the GW170817 event we have argued that if these compact stars were in galactic DM haloes with the assumption that the radius remains the same, the compactness factor can grow within the range 1/3 to 4/9 and therefore can generate gravitational waves (GW) echoes. Additionally, we have presented effect of β on the generation of GW echoes in accordance with the observational constraints related to the compact stars GW190814, PSR J0740+6620, PSR J1614−2230, Cen X-3, and LMC X-4.

Impact of polytropic fluid on a usual gravitational source

This paper investigates the outcomes of polytropic matter distribution with a gravitational source in f(T) gravity, where f(T) is torsion scalar’s arbitrary function. We study the influence of f(T) gravity on the distribution of energy between fluids in the interior of a stellar object using polytropic equation of state. We provide a comprehensive framework for determining generic relativistic polytropes by means of minimal geometric decoupling strategy. A few physical characteristics of polytropes with perfect fluids, like effective pressure, energy exchange, polytropic index, thermal properties, etc using Tolman IV solution are noticed.

Odd-Leg Birdcages for Geometric Decoupling in Multinuclear Imaging and Spectroscopy

The utility of interleaved odd-number leg birdcage coils is demonstrated for decoupling in double- and triple-tuned multinuclear applications. The birdcage was designed to geometrically decouple from a planar double-tuned (1H-23Na) array and from a 31P saddle coil insert to create a triple-tuned configuration. Comparisons between an actively detuned coil and a purely geometrically decoupled architecture were used to demonstrate the capabilities of the design. In particular cases, the simplicity and adaptability of the interleaved nine-leg design for multinuclear nuclear magnetic resonance (NMR) offer a straightforward alternative to the often complex and lossy designs currently available for multinuclear birdcages and volume coils.

Decoupled Anisotropic Solutions Using Karmarkar Condition in f(G, T) Gravity

In this paper, we compute two anisotropic static spherical solutions for two compact stellar candidates in the background of f(G,T) gravity using the minimal geometric decoupling technique. The internal structure becomes anisotropic when an additional sector is added to the isotropic system. With this method, the radial component is distorted to establish two sets of the field equations that represent perfect and anisotropic sources. We use the Karmarkar condition to formulate the metric potentials that help to find the solution of the first set. For the second set, two extra constraints are applied on theanisotropic sector to find its solution. Both of the solutions are then combined to yield the ultimate anisotropic solution. We then examine the physical feasibility and stability of the resulting anisotropic solutions through energy conditions and stability criteria, respectively. It is found that the compact star Her X-1 is viable but not stable corresponding to the first solution while satisfying all the physical acceptability conditions for the second solution. On the other hand, the star 4U 1820-30 indicates viable and stable behavior for both anisotropic solutions.

A novel collision-free NC code generation method with fixed tool orientation vector using the geometric decoupling strategy based on the three rotary axes milling head

A novel collision-free NC code generation method with fixed tool orientation vector using the geometric decoupling strategy based on the three rotary axes milling head

Experimental study on the mechanical properties of a multi-dimensional vibration control damper

The load and structural response of large-span spatial structures have obvious multi-dimensional characteristics. In contrast to double-layer structures, single-layer reticulated large-span spatial structures are usually subjected to a combination of the multi-dimensional internal force. In this study, a multi-dimensional vibration control damper (MD-damper) for single-layer reticulated large-span spatial structures was developed. The MD-damper provided multi-dimensional carrying capacity and achieved vibration control. The theoretical analysis of the mechanical properties of the damper was performed. The vibration reduction mechanics model and the theoretical formula of the restoring force calculation of the damper were derived from the geometric decoupling and mechanical analysis. A calculation program was developed for solving the theoretical formula. An experimental study on the mechanical properties of MD-damper was performed to verify the theoretical results, and the finite element software ABAQUS was used for simulation analysis. The theoretical and simulation results were compared with that of the experimental results to verify the accuracy of the theoretical formula and the applicability of the simulation analysis method. The energy consumption mechanism of the MD-damper and the effect of vibration reduction were revealed. The results exhibited that the hysteresis curves of the experimental results were in good agreement with that of the simulated data. The deviation between the theoretical and simulation results of peak restoring force was in the range of 0.34–5.00% compared with that of the experimental results. The MD-damper exhibited optimum energy consumption performance and provided effective multi-dimensional vibration reduction. Hence, MD-Damper is an effective vibration control damper that can be used for single-layer reticulated large-span spatial structures.

Azobenzene-Substituted Triptycenes: Understanding the Exciton Coupling of Molecular Switches in Close Proximity.

Herein, we report a series of azobenzene‐substituted triptycenes. In their design, these switching units were placed in close proximity, but electronically separated by a sp3 center. The azobenzene switches were prepared by Baeyer–Mills coupling as key step. The isomerization behavior was investigated by 1H NMR spectroscopy, UV/Vis spectroscopy, and HPLC. It was shown that all azobenzene moieties are efficiently switchable. Despite the geometric decoupling of the chromophores, computational studies revealed excitonic coupling effects between the individual azobenzene units depending on the connectivity pattern due to the different transition dipole moments of the π→π* excitations. Transition probabilities for those excitations are slightly altered, which is also revealed in their absorption spectra. These insights provide new design parameters for combining multiple photoswitches in one molecule, which have high potential as energy or information storage systems, or, among others, in molecular machines and supramolecular chemistry.

Relativistic charged stellar model of the Pant interior solution via gravitational decoupling and Karmarkar conditions

This paper explores a new embedding anisotropic charged version of a solution to Einstein–Maxwell field equations in four-dimensional spacetime through the Karmarkar conditions and the gravitational decoupling via minimal geometric decoupling (MGD) technique by choosing Pant’s interior solution [Astrophys. Space Sci. 331, 633 (2011)] as a seed solution to coupled system. Later, we integrate the coupled system within the MGD and explore a family of solutions to represent the realistic structure of nonrotating compact objects. Through the matching of the interior solutions so obtained to the exterior Reissner–Nordström metric, we tune the arbitrary constants for feasible models. After that, we subject our model to a rigorous test for a chosen parameter space to verify the physical viability of the solution for the neutron stars in EXO 1785-248 for a range of values of the decoupling constant [Formula: see text]. Further, we prove that the constant [Formula: see text] is inherently connected to critical physical properties such as the gravitational and surface redshifts, compactification factor, mass/radius relation, etc., of the same compact star candidate EXO 1785-248. The solutions thus obtained exhibit physically viable features which are thoroughly demonstrated through graphical plots.

Statistical mechanics of quantum error correcting codes

We study stabilizer quantum error correcting codes (QECC) generated under hybrid dynamics of local Clifford unitaries and local Pauli measurements in one dimension. Building upon 1) a general formula relating the error-susceptibility of a subregion to its entanglement properties, and 2) a previously established mapping between entanglement entropies and domain wall free energies of an underlying spin model, we propose a statistical mechanical description of the QECC in terms of "entanglement domain walls". Free energies of such domain walls generically feature a leading volume law term coming from its "surface energy", and a sub-volume law correction coming from thermodynamic entropies of its transverse fluctuations. These are most easily accounted for by capillary-wave theory of liquid-gas interfaces, which we use as an illustrative tool. We show that the information-theoretic decoupling criterion corresponds to a geometric decoupling of domain walls, which further leads to the identification of the "contiguous code distance" of the QECC as the crossover length scale at which the energy and entropy of the domain wall are comparable. The contiguous code distance thus diverges with the system size as the subleading entropic term of the free energy, protecting a finite code rate against local undetectable errors. We support these correspondences with numerical evidence, where we find capillary-wave theory describes many qualitative features of the QECC; we also discuss when and why it fails to do so.

The "Loopole" Antenna: A Hybrid Coil Combining Loop and Electric Dipole Properties for Ultra-High-Field MRI.

Purpose.To revisit the “loopole,” an unusual coil topology whose unbalanced current distribution captures both loop and electric dipole properties, which can be advantageous in ultra-high-field MRI.Methods.Loopole coils were built by deliberately breaking the capacitor symmetry of traditional loop coils. The corresponding current distribution, transmit efficiency, and signal-to-noise ratio (SNR) were evaluated in simulation and experiments in comparison to those of loops and electric dipoles at 7 T (297 MHz).Results.The loopole coil exhibited a hybrid current pattern, comprising features of both loops and electric dipole current patterns. Depending on the orientation relative to B0, the loopole demonstrated significant performance boost in either the transmit efficiency or SNR at the center of a dielectric sample when compared to a traditional loop. Modest improvements were observed when compared to an electric dipole.Conclusion.The loopole can achieve high performance by supporting both divergence-free and curl-free current patterns, which are both significant contributors to the ultimate intrinsic performance at ultra-high field. While electric dipoles exhibit similar hybrid properties, loopoles maintain the engineering advantages of loops, such as geometric decoupling and reduced resonance frequency dependence on sample loading.

Parton theory of angle-resolved photoemission spectroscopy spectra in antiferromagnetic Mott insulators

Angle-resolved photoemission spectroscopy (ARPES) has revealed peculiar properties of mobile dopants in correlated anti-ferromagnets (AFMs). But describing them theoretically, even in simplified toy models, remains a challenge. Here we study ARPES spectra of a single mobile hole in the $t-J$ model. Recent progress in the microscopic description of mobile dopants allows us to use a geometric decoupling of spin and charge fluctuations at strong couplings, from which we conjecture a one-to-one relation of the one-dopant spectral function and the spectrum of a constituting spinon in the \emph{undoped} parent AFM. We thoroughly test this hypothesis for a single hole doped into a 2D Heisenberg AFM by comparing our semi-analytical predictions to previous quantum Monte Carlo results and our large-scale time-dependent matrix product state (td-MPS) calculations of the spectral function. Our conclusion is supported by a microscopic trial wavefuntion describing spinon-chargon bound states, which captures the momentum and $t/J$ dependence of the quasiparticle residue. Our conjecture suggests that ARPES measurements in the pseudogap phase of cuprates can directly reveal the Dirac-fermion nature of the constituting spinons. Specifically, we demonstrate that our trial wavefunction provides a microscopic explanation for the sudden drop of spectral weight around the nodal point associated with the formation of Fermi arcs, assuming that additional frustration suppresses long-range AFM ordering. We benchmark our results by studying the cross-over from two to one dimension, where spinons and chargons are confined and deconfined respectively.

Development and optimization of a receive-only surface array with purely geometrical decoupling for rat brain MRI at 2 T

Magnetic resonance imaging (MRI) experiments on small animals, as well as in humans, require specific radiofrequency (RF) coil designs in order to maximize field homogeneity during excitation and signal-to-noise ratio (SNR) during reception. Therefore, the use of dedicated transmit-only and receive-only coil geometries has been preferred as standard technology configuration. Among the receive coil geometries, the surface coil has been widely used to increase the SNR in localized regions of interest. With the advent of MRI-phased arrays, the high sensitivity of surface coils can be achieved in extended regions, further allowing parallel imaging acquisition methodologies to accelerate acquisition time. This work describes the development and characterization of a two-channel receive-only RF coil set specifically designed for MRI acquisition of rat brain in a 2 T system for neuroscience studies. We have developed and compared the performance of one common surface coil with a two-channel phased array with purely geometric decoupling between coil elements (i.e., without using low input impedance preamplifiers), both actively detuned during reception and having exactly the same dimensions. The results have shown that the single-channel surface coil achieved up to 5 times higher SNR at 5 mm depth compared to a volume coil commonly used for rat brain MRI in our laboratory, while the two-channel array achieved 4 times higher SNR at the same depth, with the additional advantage of producing an extended area with higher sensitivity. In vivo brain images of anesthetized rats confirmed the SNR gain for both receive-only single-channel surface coil and two-channel array in comparison with a volume coil. We have verified that only using the partial overlapping technique does not provide sufficient isolation to eliminate mutual coupling interaction between elements, since residual coupling can still affect the coil performance.

A Lyapunov Approach to Set the Parameters of a PI-Controller to minimise Velocity Oscillations in a Permanent Magnet Synchronous Motor using Chopper Control for Electrical Vehicles

This paper deals with a parameter set up of a PI-regulator to be applied in a system for permanent magnet three-phase synchronous motors to obtain a smooth tracking dynamics even though a chopper control structure is included in the drive. High performance application of permanent magnet synchronous motors (PMSM) is increasing. In particular, application in electrical vehicles is used very much. The technique uses a geometric decoupling procedure and a Lyapunov approach to perform a PWM control to be used as a chopper. Chopper control structures are very popular because they are very cheap and easy to be realise. Nevertheless, using a chopper control structure smooth tracking dynamics could be difficult to obtain without increasing the switching frequency because of the discontinuity of the control signals. No smooth tracking dynamics lead to a not comfortable travel effect for the passengers of an electrical vehicle or, more in general, it could be difficult to generate an efficient motion planning if the tracking dynamics are not smooth. This paper presents a technique to minimise these undesired effects. The presented technique is generally applicable and could be used for other types of electrical motors, as well as for other dynamic systems with nonlinear model structure. Through simulations of a synchronous motor used in automotive applications, this paper verifies the effectiveness of the proposed method and discusses the limits of the results.

Simulation of magnetic control of the plasma shape on the DEMO tokamak

About 85% of the primary energy is currently obtained from fossil sources. In the next future, nuclear fusion can significantly contribute to energy production: the fuel is in principle unlimited and radioactive waste are short lived. Next steps in fusion research are represented by the two tokamaks ITER, which is under construction, and DEMO, which is in its conceptual design phase. In this paper we focus on a specific aspect of DEMO design, that is indeed crucial for tokamak safe operation: plasma vertical and shape control. It is well known that a plasma with elongated cross-section exhibits a vertical instability that needs to be feedback controlled. Typically on operating tokamaks, and in ITER, this task is accomplished using in-vessel actuator coils. Since in the present DEMO design these coils are not foreseen, hereafter we assumed that all the actuator coils, located outside the vessel, are used at the same time to guarantee both vertical stabilization and shape control, resorting to a suitable geometric decoupling. The performance of the controller is shown in simulation using a nonlinear evolution code during a plasma H-L back-transition.

Design of a Quadrature 1H/31P Coil Using Bent Dipole Antenna and Four-Channel Loop at 3T MRI.

MRI using nuclei other than protons is of clinical interest due to the important role of these nuclei in cellular processes. Phosphorous-31 (31P), for example, plays an important role in energy metabolism. However, measurement of 31P can be challenging, as the receive signal is weak compared with that of proton (1H). Consequently, it is often necessary to integrate 1H elements for localizations and B0 shimming in RF coils intended for 31P measurements. Good decoupling between the 1H and the 31P elements is therefore essential. In this paper, bent dipole antennas tuned to 1H were integrated with a four channel 31P loop coil array, in a manner providing strong geometric decoupling between dipoles and loops. As the physical length of a resonant dipole antenna is too long at 3T, the dipole antennas were bent around the load. The loss of 31P elements due to the presence of the dipole antennas was evaluated by measuring scattering parameters and comparing the SNR of 31P spectra with and without the presence of the dipole antennas. The performance of the bent dipole antenna was evaluated by simulation and sensitivity measurement. The Q-factors and the SNR of the four-loop array were reduced by less than 5% when the bent dipole antennas were introduced. The measured sensitivity of the bent dipole was higher (15%) than that of dual-tuned birdcage. The combined bent dipole and loop array is therefore a promising design for 1H/31P applications at 3T.

Double‐layered dual‐tuned RF coil using frequency‐selectable PIN‐diode control at 7‐T MRI

AbstractThis article presents a dual‐tuned (DT) radiofrequency (RF) coil for signal acquisition of 2 nuclei, namely, hydrogen (1H) and sodium (23Na), in the ultra‐high magnetic field of a 7‐T magnetic resonance imaging (MRI) system. The double‐layered dual‐tuned (DLDT) coil comprises a 2‐loop coil configuration per single‐pair geometry, with the 1H and 23Na coils being located on the outside and inside, respectively. The 1H and 23Na single‐pair elements are tuned to resonance frequencies of 297.20 and 78.61 MHz, respectively. The single‐pair geometry of the DLDT coil is extended to an 8‐pair configuration to cover the human head, and the operation mode is transmission/reception (Tx/Rx). The 8‐pair DLDT Tx/Rx coil array is designed with a non‐overlapped single pair between the 1H coil elements for geometric decoupling, and capacitive decoupling is implemented to minimize the mutual inductance coupling. The 2 resonance frequencies are fed through a single RF port to a common matching board, and each frequency is selected using the voltages at both ends of a PIN diode. Through use of the PIN diode in the DLDT coil configuration, with a voltage drop at both ends, different resonance frequencies can be selected for each coil element in accordance with the diode ON/OFF state. The experiments conducted showed that the proposed DLDT coil is effective in acquiring signals of 1H and 23Na in the MRI system.

Decoupled extensional faulting and forced folding in the southern part of the Roer Valley Graben, Belgium

During late Oligocene incipient rifting, the southern part of the Roer Valley Graben was characterized by normal faulting and forced folding of its Paleogene pre-rift strata. The 2D seismic data used in this study shows that these faults and forced folds were geometrically decoupled from faults or fault zones in the underlying Triassic and older strata. Geometric decoupling consistently took place in an interval that comprises (latest Triassic to Early Jurassic) soft claystones on top of (Triassic) alternations of evaporites and claystones layers. This mechanically weak interval probably inhibited the upward propagation of (re)activated underlying faults, resulting in the formation of the observed forced folds (monoclines) in the overlying Paleogene pre-rift strata. Strain from the sub-detachment faults was distributed along the mechanically weak interval towards detachment edges, leading to the consistent presence of faults in the footwall domain of the supra-detachment monoclines. The mechanically weak interval was thereby able to maintain the kinematic coherency between geometrically decoupled under- and overlying deformation throughout late Oligocene rifting.

Development of a 2-degree-of-freedom decoupled flexural mechanism for micro/nanomachining

In this article, a novel decoupled two-degree-of-freedom parallel flexural mechanism is proposed for precision engineering, such as micro/nanomeasuring and machining. The two-degree-of-freedom flexural mechanism is developed with the parallel-kinematic constraint map method to achieve totally geometric decoupling and the actuator isolation. By means of the matrix which is based on compliance modeling method, the compliance matrix of the flexural mechanism has been analytically derived and then the obtained theoretical results are verified by the finite element analysis. Experiment tests are conducted to investigate the practical performances of the developed two-degree-of-freedom flexural mechanism. The experimental results show that the maximum stroke along z-axis and y-stroke are 10.82 and 11.84 µm, respectively, and the corresponding maximum couplings in y-axis and z-axis directions are less than 3%. The first obtained resonant frequencies in the two moving directions are 420 and 450 Hz through the method of swept excitations, respectively.

Geometric decoupling of a mouse array coil using a dual plane pair design with crisscrossed return paths and custom mounting fixture.

An element design for receive array coils that decouples from the transmit coil without external active detuning is presented for magnetic resonance imaging (MRI) of mice. The array element uses a crisscrossed geometry on the return paths to reduce the current induced by the transmit coil. Without the need for an external active detune network, the proposed method simplifies the construction of MRI coil systems and also mitigates problems in space-limited MRI applications. In addition, an adaptable scissor-jack-like fixture is presented that allows the receive array to move parallel to the transmit coil to maintain the decoupling condition while maintaining close contact with varying sizes of mice.