A theory of hyperfinite sets

We develop an axiomatic set theory -- the Theory of Hyperfinite Sets THS, which is based on the idea of existence of proper subclasses of big finite sets. We demonstrate how theorems of classical continuous mathematics can be transfered to THS, prove consistency of THS and present some applications.Comment: 28 page

The Gordon-Haus effect for modified NLS solitons

Random jitter in the soliton arrival time (the Gordon-Haus effect) is analyzed for solitons being solutions of the integrable modified nonlinear Schroedinger equation. It is shown that the mean square fluctuation of the soliton position depends on the soliton parameters which can be properly adjusted to suppress the Gordon-Haus jitter.Comment: LaTeX, 7 pages, 3 figures, to be published in Europhys. Let

An Experimental Assessment of LiFi Data Communication

In this paper, two functional light fidelity real-time testbeds implemented on custom Light fidelity (LiFi) kits are presented. This paper evaluates the use of LiFi technology over differ­ent distances and angular placement of illuminating devices and endpoint transceivers with connectivity locally and to the internet. The objective is to determine if distance or angular positioning in LiFi influence speeds or not. Finally, it aims to contribute to knowledge in the LiFi communication domain. We were limited to developing a customized testbed for wireless optical communication by accessing data in the physical layer via photons. In a lateral dis­tance and angular position, we examined the performance of a laptop with LiFi activated by a 3730 lm LED. The setup evaluated the performance of our design in a downlink and uplink scenario where the transmitter was embedded in the main LED unit and the laptop was used as a photoreceiver. The data rate/kbps, the lateral distance / m, and the angle displacement / θ° were the comparison metrics. The results of the tests show that the transmission of LiFi is not influenced by distance and angular positioning for both downloads and uploads over different distances

Dynamical control of quantum state transfer within hybrid open systems

We analyze quantum state-transfer optimization within hybrid open systems, from a "noisy" (write-in) qubit to its "quiet" counterpart (storage qubit). Intriguing interplay is revealed between our ability to avoid bath-induced errors that profoundly depend on the bath-memory time and the limitations imposed by leakage out of the operational subspace. Counterintuitively, under no circumstances is the fastest transfer optimal (for a given transfer energy)

Vortex lattice stability and phase coherence in three-dimensional rapidly rotating Bose condensates

We establish the general equations of motion for the modes of a vortex lattice in a rapidly rotating Bose-Einstein condensate in three dimensions, taking into account the elastic energy of the lattice and the vortex line bending energy. As in two dimensions, the vortex lattice supports Tkachenko and gapped sound modes. In contrast, in three dimensions the Tkachenko mode frequency at long wavelengths becomes linear in the wavevector for any propagation direction out of the transverse plane. We compute the correlation functions of the vortex displacements and the superfluid order parameter for a homogeneous Bose gas of bounded extent in the axial direction. At zero temperature the vortex displacement correlations are convergent at large separation, but at finite temperatures, they grow with separation. The growth of the vortex displacements should lead to observable melting of vortex lattices at higher temperatures and somewhat lower particle number and faster rotation than in current experiments. At zero temperature a system of large extent in the axial direction maintains long range order-parameter correlations for large separation, but at finite temperatures the correlations decay with separation.Comment: 10 pages, 2 figures, Changes include the addition of the particle density - vortex density coupling and the correct value of the shear modulu

Periodic and Quasi-Periodic Compensation Strategies of Extreme Outages caused by Polarization Mode Dispersion and Amplifier Noise

Effect of birefringent disorder on the Bit Error Rate (BER) in an optical fiber telecommunication system subject to amplifier noise may lead to extreme outages, related to anomalously large values of BER. We analyze the Probability Distribution Function (PDF) of BER for various strategies of Polarization Mode Dispersion (PMD) compensation. A compensation method is proposed that is capable of more efficient extreme outages suppression, which leads to substantial improvement of the fiber system performance.Comment: 3 pages, 1 figure, Submitted to IEEE Photonics Letter

The Elephant Trunk Nebula and the Trumpler 37 cluster: Contribution of triggered star formation to the total population of an HII region

Rich young stellar clusters produce HII regions whose expansion into the nearby molecular cloud is thought to trigger the formation of new stars. However, the importance of this mode of star formation is uncertain. This investigation seeks to quantify triggered star formation (TSF) in IC 1396A (a.k.a., the Elephant Trunk Nebula), a bright rimmed cloud (BRC) on the periphery of the nearby giant HII region IC 1396 produced by the Trumpler 37 cluster. X-ray selection of young stars from Chandra X-ray Observatory data is combined with existing optical and infrared surveys to give a more complete census of the TSF population. Over 250 young stars in and around IC 1396A are identified; this doubles the previously known population. A spatio-temporal gradient of stars from the IC 1396A cloud toward the primary ionizing star HD 206267 is found. We argue that the TSF mechanism in IC 1396A is the radiation-driven implosion process persisting over several million years. Analysis of the X-ray luminosity and initial mass functions indicates that >140 stars down to 0.1 Msun were formed by TSF. Considering other BRCs in the IC 1396 HII region, we estimate the TSF contribution for the entire HII region exceeds 14-25% today, and may be higher over the lifetime of the HII region. Such triggering on the periphery of HII regions may be a significant mode of star formation in the Galaxy.Comment: Accepted for publication in MNRAS; 28 pages, 18 figure

Evaluating the climate effects of mid-1800s deforestation in New England, USA, using a Weather, Research, and Forecasting (WRF) Model Multi-Physics Ensemble

The New England region of the northeastern United States has a land use history characterized by forest clearing for agriculture and other uses during European colonization and subsequent reforestation following widespread farm abandonment. Despite these broad changes, the potential influence on local and regional climate has received relatively little attention. This study investigated wintertime (December through March) climate impacts of reforestation in New England using a high-resolution (4 km) multiphysics ensemble of the Weather Research and Forecasting Model. In general, the conversion from mid-1800s cropland/grassland to forest led to warming, but results were sensitive to physics parameterizations. The 2-m maximum temperature (T2max) was most sensitive to choice of land surface model, 2-m minimum temperature (T2min) was sensitive to radiation scheme, and all ensemble members simulated precipitation poorly. Reforestation experiments suggest that conversion of mid-1800s cropland/grassland to present-day forest warmed T2max +0.5 to +3 K, with weaker warming during a warm, dry winter compared to a cold, snowy winter. Warmer T2max over forests was primarily the result of increased absorbed shortwave radiation and increased sensible heat flux compared to cropland/grassland. At night, T2min warmed +0.2 to +1.5 K where deciduous broadleaf forest replaced cropland/grassland, a result of decreased ground heat flux. By contrast, T2min of evergreen needleleaf forest cooled –0.5 to –2.1 K, primarily owing to increased ground heat flux and decreased sensible heat flux