Lifshitz-like systems and AdS null deformations

Following arXiv:1005.3291 [hep-th], we discuss certain lightlike deformations of $AdS_5\times X^5$ in Type IIB string theory sourced by a lightlike dilaton $\Phi(x^+)$ dual to the N=4 super Yang-Mills theory with a lightlike varying gauge coupling. We argue that in the case where the $x^+$-direction is noncompact, these solutions describe anisotropic 3+1-dim Lifshitz-like systems with a potential in the $x^+$-direction generated by the lightlike dilaton. We then describe solutions of this sort with a linear dilaton. This enables a detailed calculation of 2-point correlation functions of operators dual to bulk scalars and helps illustrate the spatial structure of these theories. Following this, we discuss a nongeometric string construction involving a compactification along the $x^+$-direction of this linear dilaton system. We also point out similar IIB axionic solutions. Similar bulk arguments for $x^+$-noncompact can be carried out for deformations of $AdS_4\times X^7$ in M-theory.Comment: Latex, 20pgs, 1 eps fig; v2. references added; v3. minor clarifications added, to appear in PR

Self similar Barkhausen noise in magnetic domain wall motion

A model for domain wall motion in ferromagnets is analyzed. Long-range magnetic dipolar interactions are shown to give rise to self-similar dynamics when the external magnetic field is increased adiabatically. The power spectrum of the resultant Barkhausen noise is of the form $1/\omega^\alpha$, where $\alpha\approx 1.5$ can be estimated from the critical exponents for interface depinning in random media.Comment: 7 pages, RevTex. To appear in Phys. Rev. Let

Numeričko istraživanje efekta otoka na Rayleigheve valove

To improve our understanding of Rayleigh wave generation and propagation in oceans, the effects of the presence of an island on the Rayleigh wave features are simulated. The analysis of results reveals Rayleigh wave generation in ocean near the island. In the water column, a decrease of amplitude in the vertical component and an increase of amplitude in the radial component of Rayleigh wave with depth are observed. The path of particle motion is elliptical clockwise, vertically polarised at the surface and horizontally polarised at the base of the water column. An increase of Rayleigh wave amplitude with island-slope (20° – 60°) is obtained, in contrast to the decrease of Rayleigh wave amplitude with increase of slope of basin-edge in the basin.. The effect of island-slope is greater in the vertical component, as compared to the radial one. Responses of different submersed islands (0 – 75 m below water surface) reveal decrease of amplitude of island-induced Rayleigh waves with depth. The obtained results help us to understand the characteristics and the generation of Rayleigh waves near islands.Kako bismo poboljšali razumijevanje nastanka i rasprostiranja Rayleighevih valova u oceanima simulirani su efekti otoka na obilježja Rayleigevih valova. Analizom rezultata pokazano je da se u oceanu u blizini otoka stvaraju Rayleighevi valovi. U vodenom stupcu se primjećuje smanjenje amplitude vertikalne komponente i povećanje amplitude radijalne komponente Raylieghevih valova s dubinom. Čestica se giba eliptično u smjeru gibanja kazaljke na satu, vertikalno je polarizirana na površini i horizontalno na dnu vodenog stupca. Zapaženo je povećanje amplitude Rayleighevog vala s nagibom otoka (20°–60°); nasuprot tome amplituda Rayleighevog vala u bazenu smanjuje se s povećanjem nagiba ruba bazena. Efekt nagiba otoka je ve}i u vertikalnoj komponenti nego u radijalnoj. Odziv različitih podvodnih otoka (0–75 m ispod površine vode) ukazuje na smanjenje amplitude s dubinom kod otokom induciranih Rayleighevih valova

Free energies in the presence of electric and magnetic fields

We discuss different free energies for materials in static electric and magnetic fields. We explain what the corresponding Hamiltonians are, and describe which choice gives rise to which result for the free energy change, dF, in the thermodynamic identity. We also discuss which Hamiltonian is the most appropriate for calculations using statistical mechanics, as well as the relationship between the various free energies and the "Landau function", which has to be minimized to determine the equilibrium polarization or magnetization, and is central to Landau's theory of second order phase transitions

H/V spektralni omjer i faktor amplifikacije: numerički eksperiment pomoću 2.5-D modeliranja

This paper presents the H/V ratio peak amplitude and frequency, their correlation with the site frequency and amplification factor, and limitations. The basin-edge and flat-layer models with different types of soils in the surficial layer were simulated using 2.5D (two and half dimensional) modelling. The effects of sediment bedrock velocity contrast on the H/V ratio peak frequency and amplitude, and the sensitivity of the H/V ratio peak to both the S-wave transfer function and the ellipticity of Rayleigh waves at the fundamental frequency were studied. Simulated results revealed that H/V ratio peak frequencies for both the basin-edge and flat-layer models were in good agreement with the soils fundamental frequencies, only when velocity contrast was larger than 3.5. The comparison of H/V ratio peak amplitude and amplification factors indicates that the use of amplitude of H/V ratio as amplification factor of soil/site is not justified because the obtained H/V ratio was not in accordance with the velocity contrast and can have any value independent of soil velocity and was not similar in magnitude for radial and transverse components. Analysis of the H/V ratio and spectral amplitudes of responses of basin-edge and flat-layer models revealed that it was the trapping of waves (body waves or surface waves) which was responsible for the spectral peak in the H/V ratio at the fundamental frequency. It was also concluded that surface waves were generated near the edge of the basin and propagated normal to the edge, towards the basin. The peak amplification factors were found in good agreement with the fundamental frequency of soil beneath respective recording stations.Razmotren je omjer spektara horizontalne i vertikalne komponente (H/V) gibanja tla, najveća spektralna amplituda i odgovarajuća frekvencija te njihov odnos s karakterističnom frekvencijom i amplifikacijom površinskih slojeva tla. Koristeći 2.5-D modeliranje, simulirani su uvjeti ruba bazena kao i model s horizontalnim sedimentnim slojevima. Proučen je utjecaj kontrasta brzina seizmičkih valova na amplitudu i frekvenciju H/V spektralnog šiljka, kao i njihovu osjetljivost na prijenosnu funkciju S-valova i na eliptičnost Rayleighevih valova u pojedinom modelu. Simulirani rezultati pokazuju da dominantna frekvencija H/V spektra u obje vrste modela odgovara osnovnoj frekvenciji modela samo kad je kontrast brzina između osnovne stijene i slojeva veći od 3.5. Analiza također pokazuje da nije opravdano korištenje H/V spektralnih omjera za procjenu amplifikacijskog spektra, jer nije opažena korelacija između teorijskih amplifikacijskih spektara i simuliranih H/V spektralnih omjera, koji su se čak razlikovali i za radijalnu i transverzalnu horizontalnu komponentu

H/V spektralni omjer i faktor amplifikacije: numerički eksperiment pomoću 2.5-D modeliranja

This paper presents the H/V ratio peak amplitude and frequency, their correlation with the site frequency and amplification factor, and limitations. The basin-edge and flat-layer models with different types of soils in the surficial layer were simulated using 2.5D (two and half dimensional) modelling. The effects of sediment bedrock velocity contrast on the H/V ratio peak frequency and amplitude, and the sensitivity of the H/V ratio peak to both the S-wave transfer function and the ellipticity of Rayleigh waves at the fundamental frequency were studied. Simulated results revealed that H/V ratio peak frequencies for both the basin-edge and flat-layer models were in good agreement with the soils fundamental frequencies, only when velocity contrast was larger than 3.5. The comparison of H/V ratio peak amplitude and amplification factors indicates that the use of amplitude of H/V ratio as amplification factor of soil/site is not justified because the obtained H/V ratio was not in accordance with the velocity contrast and can have any value independent of soil velocity and was not similar in magnitude for radial and transverse components. Analysis of the H/V ratio and spectral amplitudes of responses of basin-edge and flat-layer models revealed that it was the trapping of waves (body waves or surface waves) which was responsible for the spectral peak in the H/V ratio at the fundamental frequency. It was also concluded that surface waves were generated near the edge of the basin and propagated normal to the edge, towards the basin. The peak amplification factors were found in good agreement with the fundamental frequency of soil beneath respective recording stations.Razmotren je omjer spektara horizontalne i vertikalne komponente (H/V) gibanja tla, najveća spektralna amplituda i odgovarajuća frekvencija te njihov odnos s karakterističnom frekvencijom i amplifikacijom površinskih slojeva tla. Koristeći 2.5-D modeliranje, simulirani su uvjeti ruba bazena kao i model s horizontalnim sedimentnim slojevima. Proučen je utjecaj kontrasta brzina seizmičkih valova na amplitudu i frekvenciju H/V spektralnog šiljka, kao i njihovu osjetljivost na prijenosnu funkciju S-valova i na eliptičnost Rayleighevih valova u pojedinom modelu. Simulirani rezultati pokazuju da dominantna frekvencija H/V spektra u obje vrste modela odgovara osnovnoj frekvenciji modela samo kad je kontrast brzina između osnovne stijene i slojeva veći od 3.5. Analiza također pokazuje da nije opravdano korištenje H/V spektralnih omjera za procjenu amplifikacijskog spektra, jer nije opažena korelacija između teorijskih amplifikacijskih spektara i simuliranih H/V spektralnih omjera, koji su se čak razlikovali i za radijalnu i transverzalnu horizontalnu komponentu

Simulacija snažne trešnje tla pomoću smičnih dislokacijskih izvora

Paper presents the generation and implementation of various types of earthquake sources in a 2D finite difference grid. The procedure used for computing dislocations on the fault plane is identical to both well known kinematic and dynamic models, since it was calculated by solving the equation of motion taking into account the stress drop and the shear strength of the fault. This scheme is superior over the kinematic model because it calculates dislocation using stress drop instead of taking a priori dislocation pattern without any physical reasoning. Unlike the dynamic model, it does not require driving and resisting forces. The parsimonious staggered grid method was adopted instead of the conventional staggered grid since it requires less computational memory and enjoys the same advantage of being stable for larger Poisson\u27s ration, and free from spatial derivative of elastic parameters. Further, this scheme is flexible and allows a simple way of incorporating stress-free boundary condition. The algorithms were written for the simulation of P-SV and SH-waves propagation. The computed radiation patterns of the various earthquake sources for P-SV and SH-waves are in good agreement with the analytical radiation patterns. The effects of soil thickness and the velocity within it were studied in detail since they play an important role in the amplitude amplification, changes in signal duration, frequency content and mode conversion. Results depict that for the steeply incident waves, the impedance decrease and resonance effects control the amplitude amplification. The mode conversion at interfaces and multiple reflections in the surficial layer increase the signal duration.U radu je razmotreno zračenje različitih vrsta potresnih izvora pomoću metode konačnih razlika u dvodimenzionalnoj mreži. Rabljeni postupak daje jednake rezultate kao dobro poznati kinematički i dinamički modeli, jer se račun provodi rješavanjem jednadžbi gibanja uzimajući u obzir pad napetosti i otpornost na smicanje po rasjednoj plohi. Rabljena je shema superiorna kinematičkom modelu jer se pomaci računaju pomoću pada napetosti umjesto korištenjem unaprijed zadane razdiobe pomaka bez ikakve fizikalne podloge. Prednost u odnosu na dinamički model je da nije potrebno pretpostaviti nikakvu vanjsku silu. Rabljena shema je fleksibilna i omogućuje jednostavno uvođenje rubnih uvjeta na granicama modela. Napisani su algoritmi za simulaciju rasprostiranja P-SV i SH valova. Izračunate razdiobe pomaka za razne potresne izvore u suglasju su s analitičkim rješenjima. Detaljno je razmotren utjecaj debljine površinskog sloja i pretpostavljene brzine rasprostiranja elastičkih valova, koji imaju velik utjecaj na amplifikaciju, trajanje signala, frekventni sadržaj i konverziju modova. Rezultati ukazuju da je amplifikacija u slučaju strmo-upadajućih valova kontrolirana smanjenjem impedancije i rezonantnim efektima. Konverzija modova na diskontinuitetima i višestruke refleksije povećavaju trajanje signala

Determining the sign of Δ31\Delta_{31} at long baseline neutrino experiments

Recently it is advocated that high intensity and low energy $(E_\nu \sim 2 GeV)$ neutrino beams should be built to probe the $(13)$ mixing angle $\phi$ to a level of a few parts in $10^4$. Experiments using such beams will have better signal to background ratio in searches for $\nu_\mu \to \nu_e$ oscillations. We propose that such experiments can also determine the sign of $\Delta_{31}$ even if the beam consists of {\it neutrinos} only. By measuring the $\nu_\mu \to \nu_e$ transitions in two different energy ranges, the effects due to propagation of neutrinos through earth's crust can be isolated and the sign of $\Delta_{31}$ can be determined. If the sensitivity of an experiment to $\phi$ is $\epsilon$, then the same experiment is automatically sensitive to matter effects and the sign of $\Delta_{31}$ for values of $\phi \geq 2 \epsilon$.Comment: Title changed and paper rewritten. 4 pages, 1 figure, revte

Extracting black-hole rotational energy: The generalized Penrose process

In the case involving particles the necessary and sufficient condition for the Penrose process to extract energy from a rotating black hole is absorption of particles with negative energies and angular momenta. No torque at the black-hole horizon occurs. In this article we consider the case of arbitrary fields or matter described by an unspecified, general energy-momentum tensor $T_{\mu \nu}$ and show that the necessary and sufficient condition for extraction of a black hole's rotational energy is analogous to that in the mechanical Penrose process: absorption of negative energy and negative angular momentum. We also show that a necessary condition for the Penrose process to occur is for the Noether current (the conserved energy-momentum density vector) to be spacelike or past directed (timelike or null) on some part of the horizon. In the particle case, our general criterion for the occurrence of a Penrose process reproduces the standard result. In the case of relativistic jet-producing "magnetically arrested disks" we show that the negative energy and angular-momentum absorption condition is obeyed when the Blandford-Znajek mechanism is at work, and hence the high energy extraction efficiency up to $\sim 300\%$ found in recent numerical simulations of such accretion flows results from tapping the black hole's rotational energy through the Penrose process. We show how black-hole rotational energy extraction works in this case by describing the Penrose process in terms of the Noether current.Comment: 24 pages, 14 figures, version published in Phys. Rev.