Dynamic symmetry loss of high-frequency hysteresis loops in single-domain particles with uniaxial anisotropy

Understanding how magnetic materials respond to rapidly varying magnetic fields, as in dynamic hysteresis loops, constitutes a complex and physically interesting problem. But in order to accomplish a thorough investigation, one must necessarily consider the effects of thermal fluctuations. Albeit being present in all real systems, these are seldom included in numerical studies. The notable exceptions are the Ising systems, which have been extensively studied in the past, but describe only one of the many mechanisms of magnetization reversal known to occur. In this paper we employ the Stochastic Landau-Lifshitz formalism to study high-frequency hysteresis loops of single-domain particles with uniaxial anisotropy at an arbitrary temperature. We show that in certain conditions the magnetic response may become predominantly out-of-phase and the loops may undergo a dynamic symmetry loss. This is found to be a direct consequence of the competing responses due to the thermal fluctuations and the gyroscopic motion of the magnetization. We have also found the magnetic behavior to be exceedingly sensitive to temperature variations, not only within the superparamagnetic-ferromagnetic transition range usually considered, but specially at even lower temperatures, where the bulk of interesting phenomena is seen to take place.     

Process rheokinetics and microstructure of recycled EVA/LDPE-modified bitumen

Knowledge of the kinetics of the manufacturing process of polymer–bitumen blends is of great interest because it provides information on the behaviour of the binder at different stages of the mixing operation, which is useful for the establishment of the optimum processing conditions, involving temperature and operation time. The purpose of this research was to study the evolution of the rheological properties and microstructure of a polymer-modified bitumen during its processing. A 60/70-penetration grade bitumen and recycled EVA/LDPE were mixed under different processing conditions. Measurements of the evolution of viscosity with time, at different temperatures and agitation speeds, were carried out with an experimental device known as ‘rheomixer’, that is, a helical ribbon impeller inside a mixing vessel coupled with the transducer and motor of a conventional rheometer. Under the experimental conditions selected (within the laminar region, Re<10), temperature is the most important processing variable. Hence, low agitation speeds and a processing temperature of around 180°C should be chosen for bitumen modification with the polymer used.     

Determination of dynamic fracture-initiation toughness using three-point bending tests in a modified Hopkinson pressure bar

We present a procedure for measuring the dynamic fracture-initiation toughness of materials. The method is based on three-point bending tests at high loading rates, performed in an experimental device which is a modification of the classical split Hopkinson pressure bar. Coupled with the loading device, a high-speed photography system was used to measure the crack mouth opening displacement (CMOD) directly on the specimen. The stress intensity factor was calculated by three different simplified methods and the time to fracture was obtained from an appropriate specimen instrumentation. To evaluate the results derived from the simplified methods, a two-dimensional full-numerical analysis of the dynamic bending fracture test was made. The model includes the specimen, the input bar, the impacting projectile and the supporting device and takes into account the possible loss of contact during the experiment between the input bar and the specimen and between the specimen and its supports. From the tests and numerical results, it can be concluded that the CMOD procedure, together with the knowledge of the time to fracture determined using crack gages, seems to be the best method for measuring dynamic fracture-initiation toughness.     

Highly accelerated aortic 4D flow MR imaging with variable-density random undersampling

Purpose

To investigate an effective time-resolved variable-density random undersampling scheme combined with an efficient parallel image reconstruction method for highly accelerated aortic 4D flow MR imaging with high reconstruction accuracy.

Materials and Methods

Variable-density Poisson-disk sampling (vPDS) was applied in both the phase-slice encoding plane and the temporal domain to accelerate the time-resolved 3D Cartesian acquisition of flow imaging. In order to generate an improved initial solution for the iterative self-consistent parallel imaging method (SPIRiT), a sample-selective view sharing reconstruction for time-resolved random undersampling (STIRRUP) was introduced. The performance of different undersampling and image reconstruction schemes were evaluated by retrospectively applying those to fully sampled data sets obtained from three healthy subjects and a flow phantom.

Results

Undersampling pattern based on the combination of time-resolved vPDS, the temporal sharing scheme STIRRUP, and parallel imaging SPIRiT, were able to achieve 6-fold accelerated 4D flow MRI with high accuracy using a small number of coils (N = 5). The normalized root mean square error between aorta flow waveforms obtained with the acceleration method and the fully sampled data in three healthy subjects was 0.04 ± 0.02, and the difference in peak-systolic mean velocity was − 0.29 ± 2.56 cm/s.

Conclusion

Qualitative and quantitative evaluation of our preliminary results demonstrate that time-resolved variable-density random sampling is efficient for highly accelerating 4D flow imaging while maintaining image reconstruction accuracy.     

Harada–Tsutsui gauge recovery procedure: From Abelian gauge anomalies to the Stueckelberg mechanism

Revisiting a path-integral procedure developed by Harada and Tsutsui for recovering gauge invariance from anomalous effective actions, it is shown that there are two ways to achieve gauge symmetry: one already presented by the authors, which is shown to preserve the anomaly in the sense of standard current conservation law, and another one which is anomaly-free, preserving current conservation. It is also shown that the application of the Harada–Tsutsui technique to other models which are not anomalous but do not exhibit gauge invariance allows the identification of the gauge invariant formulation of the Proca model, also done by the referred authors, with the Stueckelberg model, leading to the interpretation of the gauge invariant map as a generalization of the Stueckelberg mechanism.     

On gravity localization in scalar braneworlds with a super-exponential warp factor

The optical medium analogy of a given spacetime was developed decades ago and has since then been widely applied to different gravitational contexts. Here we consider the case of a colliding gravitational wave spacetime, generalizing previous results concerning single gravitational pulses. Given the complexity of the nonlinear interaction of two gravitational waves in the framework of general relativity, typically leading to the formation of either horizons or singularities, the optical medium analogy proves helpful to simply capture some interesting effects of photon propagation.     

Asymptotic Behavior of the Maximum and Minimum Singular Value of Random Vandermonde Matrices

This study examines various statistical distributions in connection with random Vandermonde matrices and their extension to \(d\) -dimensional phase distributions. Upper and lower bound asymptotics for the maximum singular value are found to be \(O(\log ^{1/2}{N^{d}})\) and \(\Omega ((\log N^{d} /(\log \log N^d))^{1/2})\) , respectively, where \(N\) is the dimension of the matrix, generalizing the results in Tucci and Whiting (IEEE Trans Inf Theory 57(6):3938–3954, 2011). We further study the behavior of the minimum singular value of these random matrices. In particular, we prove that the minimum singular value is at most \(N\exp (-C\sqrt{N}))\) with high probability where \(C\) is a constant independent of \(N\) . Furthermore, the value of the constant \(C\) is determined explicitly. The main result is obtained in two different ways. One approach uses techniques from stochastic processes and in particular a construction related to the Brownian bridge. The other one is a more direct analytical approach involving combinatorics and complex analysis. As a consequence, we obtain a lower bound for the maximum absolute value of a random complex polynomial on the unit circle, which may be of independent mathematical interest. Lastly, for each sequence of positive integers \(\{k_p\}_{p=1}^{\infty }\) we present a generalized version of the previously discussed matrices. The classical random Vandermonde matrix corresponds to the sequence \(k_{p}=p-1\) . We find a combinatorial formula for their moments and show that the limit eigenvalue distribution converges to a probability measure supported on \([0,\infty )\) . Finally, we show that for the sequence \(k_p=2^{p}\) the limit eigenvalue distribution is the famous Marchenko–Pastur distribution.