Generating sequences and Poincar\'e series for a finite set of plane divisorial valuations

Let $V$ be a finite set of divisorial valuations centered at a 2-dimensional regular local ring $R$. In this paper we study its structure by means of the semigroup of values, $S_V$, and the multi-index graded algebra defined by $V$, \gr_V R. We prove that $S_V$ is finitely generated and we compute its minimal set of generators following the study of reduced curve singularities. Moreover, we prove a unique decomposition theorem for the elements of the semigroup. The comparison between valuations in $V$, the approximation of a reduced plane curve singularity $C$ by families of sets $V^{(k)}$ of divisorial valuations, and the relationship between the value semigroup of $C$ and the semigroups of the sets $V^{(k)}$, allow us to obtain the (finite) minimal generating sequences for $C$ as well as for $V$. We also analyze the structure of the homogeneous components of \gr_V R. The study of their dimensions allows us to relate the Poincar\'e series for $V$ and for a general curve $C$ of $V$. Since the last series coincides with the Alexander polynomial of the singularity, we can deduce a formula of A'Campo type for the Poincar\'e series of $V$. Moreover, the Poincar\'e series of $C$ could be seen as the limit of the series of $V^{(k)}$, $k\ge 0$

Spin dynamics of current driven single magnetic adatoms and molecules

A scanning tunneling microscope can probe the inelastic spin excitations of a single magnetic atom in a surface via spin-flip assisted tunneling in which transport electrons exchange spin and energy with the atomic spin. If the inelastic transport time, defined as the average time elapsed between two inelastic spin flip events, is shorter than the atom spin relaxation time, the STM current can drive the spin out of equilibrium. Here we model this process using rate equations and a model Hamiltonian that describes successfully spin flip assisted tunneling experiments, including a single Mn atom, a Mn dimer and Fe Phthalocyanine molecules. When the STM current is not spin polarized, the non-equilibrium spin dynamics of the magnetic atom results in non-monotonic $dI/dV$ curves. In the case of spin polarized STM current, the spin orientation of the magnetic atom can be controlled parallel or anti-parallel to the magnetic moment of the tip. Thus, spin polarized STM tips can be used both to probe and to control the magnetic moment of a single atom.Comment: 15 pages, 12 figure

A cotunneling mechanism for all-electrical Electron Spin Resonance of single adsorbed atoms

The recent development of all-electrical electron spin resonance (ESR) in a scanning tunneling microscope (STM) setup has opened the door to vast applications. Despite the fast growing number of experimental works on STM-ESR, the fundamental principles remains unclear. By using a cotunneling picture, we show that the spin resonance signal can be explained as a time-dependent variation of the tunnel barrier induced by the alternating electric driving field. We demonstrate how this variation translates into the resonant frequency response of the direct current. Our cotunneling theory explains the main experimental findings. Namely, the linear dependence of the Rabi flop rate with the alternating bias amplitude, the absence of resonant response for spin-unpolarized currents, and the weak dependence on the actual atomic species.Comment: 11 pages, 3 figure

Investigating Fatigue Performance on the Foamed Asphalt Specimens Generated Using Different Foam Properties

An evaluation of fatigue resistance for foamed asphalt mixture is very demanding since the binder is not continuously distributed on the aggregate surface and this mixtures contains water, the content of which dramatically affects the mechanical properties. This paper discusses the results of laboratory fatigue testingon the foamed asphalt mixtures in which the specimens are generated using three different foamed bitumen properties. Foamed bitumen as the binder was produced at three different foaming water content (FWC) at a temperature of 180oC using a 70/100 pen. The aggregates were mechanically mixed with foamed bitumen using a Hobart mixer. The resulting mixtures were then compacted using a gyratory compactor to generatespecimen with diameter of 100 mm. The specimens were fatigue tested at various stress levels at a temperature of 20oC following a curing period of 3 days at 40oC. Overall, fatigue performance of foamed asphalt can be identified based upon both stress and strain for mixtures produced at FWC 1%, 5%, and 10%

Quantum control on entangled bipartite qubits

Ising interaction between qubits could produce distortion in entangled pairs generated for engineering purposes (as in quantum computation) in presence of parasite magnetic fields, destroying or altering the expected behavior of process in which is projected to be used. Quantum control could be used to correct that situation in several ways. Sometimes the user should be make some measurement upon the system to decide which is the best control scheme; other posibility is try to reconstruct the system using similar procedures without perturbate it. In the complete pictures both schemes are present. We will work first with pure systems studying advantages of different procedures. After, we will extend these operations when time of distortion is uncertain, generating a mixed state, which needs to be corrected by suposing the most probably time of distortion.Comment: 10 pages, 5 figure

Storage of classical information in quantum spins

Digital magnetic recording is based on the storage of a bit of information in the orientation of a magnetic system with two stable ground states. Here we address two fundamental problems that arise when this is done on a quantized spin: quantum spin tunneling and back-action of the readout process. We show that fundamental differences exist between integer and semi-integer spins when it comes to both, read and record classical information in a quantized spin. Our findings imply fundamental limits to the miniaturization of magnetic bits and are relevant to recent experiments where spin polarized scanning tunneling microscope reads and records a classical bit in the spin orientation of a single magnetic atom

Equivariant Poincar\'e series of filtrations and topology

Earlier, for an action of a finite group $G$ on a germ of an analytic variety, an equivariant $G$-Poincar\'e series of a multi-index filtration in the ring of germs of functions on the variety was defined as an element of the Grothendieck ring of $G$-sets with an additional structure. We discuss to which extend the $G$-Poincar\'e series of a filtration defined by a set of curve or divisorial valuations on the ring of germs of analytic functions in two variables determines the (equivariant) topology of the curve or of the set of divisors

Active Learning Metamodels for ATM Simulation Modeling

Transportation systems are particularly prone to exhibiting overwhelming complexity on account of the numerous involved variables and their interrelationships, unknown stochastic phenomena, and ultimately human behavior. Simulation approaches are commonly used tools to describe and study such intricate real-world systems. Despite their obvious advantages,simulation models can still end up being quite complex themselves. The field of Air Traffic Management (ATM) modeling is no stranger to such concerns, as it traditionally involves laborious and systematic analyses built upon computationally heavy simulation models. This rather frequent shortcoming can be addressed by employing simulation metamodels combined with active learning strategies to approximate the input-output mappings inherently defined by the simulation models in an efficient way. In this work, we propose an exploration framework that integrates active learning and simulation metamodeling in a single unified approach to address recurrent computational bottlenecks typically associated with intense performance impact assessments within the field of ATM. Our methodology is designed to systematically explore the simulation input space in an efficient and self-guided manner, ultimately providing ATM practitioners with meaningful insights concerning the simulation models under study. Using a fully developed state-of-the-art ATM simulator and employing a Gaussian Process as a metamodel, we show that active learning is indeed capable of enhancing both the modeling and performances of simulation metamodeling by strategically avoiding redundant computer experiments and predicting simulation outputs values