Searcharxiv⌕ Search

arXiv subjects

Feng Guo

Publications and source records attributed to Feng Guo.

82 records · Page 5Linked to original sources
arXiv2016

Optically Detected Ferromagnetic Resonance in Metallic Ferromagnets via Nitrogen Vacancy Centers in Diamond

We report quantitative measurements of optically detected ferromagnetic resonance (ODFMR) of ferromagnetic thin films that use nitrogen-vacancy (NV) centers in diamonds to transduce FMR into a fluorescence intensity variation. To uncover the mechanism responsible for these signals, we study ODFMR as we 1) vary the separation of the NV centers from the ferromagnet (FM), 2) record the NV center longitudinal relaxation time $T_1$ during FMR, and 3) vary the material properties of the FM. Based on the results, we propose the following mechanism for ODFMR. Decay and scattering of the driven, uniform FMR mode results in spinwaves that produce fluctuating dipolar fields in a spectrum of frequencies. When the spinwave spectrum overlaps the NV center ground-state spin resonance frequencies, the dipolar fields from these resonant spinwaves relax the NV center spins, resulting in an ODFMR signal. These results lay the foundation for an approach to NV center spin relaxometry to study FM dynamics without the constraint of directly matching the NV center spin-transition frequency to the magnetic system of interest, thus enabling an alternate modality for scanned-probe magnetic microscopy that can sense ferromagnetic resonance with nanoscale resolution.

cond-mat.mes-hall↗
arXiv2015

Ferromagnetic resonance phase imaging in spin Hall multilayers

We experimentally image the magnetic precession phase of patterned spin Hall multilayer samples to study the rf driving field vector using time-resolved anomalous Nernst effect (TRANE) microscopy. Our ferromagnetic resonance (FMR) measurements quantify the phase and amplitude for both the magnetic precession and the electric current, which allows us to establish the total driving field orientation and the strength of spin Hall effect. In a channel of uniform width, we observe spatial variation of the FMR phase laterally across the channel. We interpret our findings in the context of electrical measurement using the spin-transfer torque ferromagnetic resonance technique and show that observed phase variation introduces a systematic correction into the spin Hall angle if spatial phase and amplitude variations are not taken into account.

cond-mat.mtrl-sci↗
arXiv2015

Phase-sensitive imaging of ferromagnetic resonance using ultrafast heat pulses

Measuring local magnetization dynamics and its spatial variation is essential for advancements in spintronics and relevant applications. Here we demonstrate a phase-sensitive imaging technique for studying patterned magnetic structures based on picosecond laser heating. With the time-resolved anomalous Nernst effect (TRANE) and extensions, we simultaneously image the dynamic magnetization and RF driving current density. The stroboscopic detection implemented in TRANE microscopy provides access to both amplitude and phase information of ferromagnetic resonance (FMR) and RF current. Using this approach, we measure the spatial variation of the Oersted driving field angle across a uniform channel. In a spatially nonuniform sample with a cross shape, a strong spatial variation for the RF current as well as FMR precession is observed. We find that both the amplitude and the phase of local FMR precession are closely related to those of the RF current.

cond-mat.mtrl-sci↗
arXiv2014

Semidefinite representations of non-compact convex sets

We consider the problem of the semidefinite representation of a class of non-compact basic semialgebraic sets. We introduce the conditions of pointedness and closedness at infinity of a semialgebraic set and show that under these conditions our modified hierarchies of nested theta bodies and Lasserre's relaxations converge to the closure of the convex hull of $S$. Moreover, if the PP-BDR property is satisfied, our theta body and Lasserre's relaxation are exact when the order is large enough; if the PP-BDR property does not hold, our hierarchies convergent uniformly to the closure of the convex hull of $S$ restricted to every fixed ball centered at the origin. We illustrate through a set of examples that the conditions of pointedness and closedness are essential to ensure the convergence. Finally, we provide some strategies to deal with cases where the conditions of pointedness and closedness are violated.

math.OC↗
arXiv2013

Semidefinite relaxations for semi-infinite polynomial programming

This paper studies how to solve semi-infinite polynomial programming (SIPP) problems by semidefinite relaxation method. We first introduce two SDP relaxation methods for solving polynomial optimization problems with finitely many constraints. Then we propose an exchange algorithm with SDP relaxations to solve SIPP problems with compact index set. At last, we extend the proposed method to SIPP problems with noncompact index set via homogenization. Numerical results show that the algorithm is efficient in practice.

math.OC↗
arXiv2012

Minimizing Rational Functions by Exact Jacobian SDP Relaxation Applicable to Finite Singularities

This paper considers the optimization problem of minimizing a rational function. We reformulate this problem as polynomial optimization by the technique of homogenization. These two problems are shown to be equivalent under some generic conditions. The exact Jacobian SDP relaxation method proposed by Nie is used to solve the resulting polynomial optimization. We also prove that the assumption of nonsingularity in Nie's method can be weakened as the finiteness of singularities. Some numerical examples are given to illustrate the efficiency of our method.

math.OC↗
arXiv2012

Certificates of Impossibility of Hilbert-Artin Representations of a Given Degree for Definite Polynomials and Functions

We deploy numerical semidefinite programming and conversion to exact rational inequalities to certify that for a positive semidefinite input polynomial or rational function, any representation as a fraction of sums-of-squares of polynomials with real coefficients must contain polynomials in the denominator of degree no less than a given input lower bound. By Artin's solution to Hilbert's 17th problems, such representations always exist for some denominator degree. Our certificates of infeasibility are based on the generalization of Farkas's Lemma to semidefinite programming. The literature has many famous examples of impossibility of SOS representability including Motzkin's, Robinson's, Choi's and Lam's polynomials, and Reznick's lower degree bounds on uniform denominators, e.g., powers of the sum-of-squares of each variable. Our work on exact certificates for positive semidefiniteness allows for non-uniform denominators, which can have lower degree and are often easier to convert to exact identities. Here we demonstrate our algorithm by computing certificates of impossibilities for an arbitrary sum-of-squares denominator of degree 2 and 4 for some symmetric sextics in 4 and 5 variables, respectively. We can also certify impossibility of base polynomials in the denominator of restricted term structure, for instance as in Landau's reduction by one less variable.

math.OC↗
arXiv2011

SDPTools: High Precision SDP Solver in Maple

Semidefinite programs are an important class of convex optimization problems. It can be solved efficiently by SDP solvers in Matlab, such as SeDuMi, SDPT3, DSDP. However, since we are running fixed precision SDP solvers in Matlab, for some applications, due to the numerical error, we can not get good results. SDPTools is a Maple package to solve SDP in high precision. We apply SDPTools to the certification of the global optimum of rational functions. For the Rumps Model Problem, we obtain the best numerical results so far.

math.OC↗
arXiv2008

A hierarchical Bayesian approach for estimating the origin of a mixed population

We propose a hierarchical Bayesian model to estimate the proportional contribution of source populations to a newly founded colony. Samples are derived from the first generation offspring in the colony, but mating may occur preferentially among migrants from the same source population. Genotypes of the newly founded colony and source populations are used to estimate the mixture proportions, and the mixture proportions are related to environmental and demographic factors that might affect the colonizing process. We estimate an assortative mating coefficient, mixture proportions, and regression relationships between environmental factors and the mixture proportions in a single hierarchical model. The first-stage likelihood for genotypes in the newly founded colony is a mixture multinomial distribution reflecting the colonizing process. The environmental and demographic data are incorporated into the model through a hierarchical prior structure. A simulation study is conducted to investigate the performance of the model by using different levels of population divergence and number of genetic markers included in the analysis. We use Markov chain Monte Carlo (MCMC) simulation to conduct inference for the posterior distributions of model parameters. We apply the model to a data set derived from grey seals in the Orkney Islands, Scotland. We compare our model with a similar model previously used to analyze these data. The results from both the simulation and application to real data indicate that our model provides better estimates for the covariate effects.

stat.AP↗