Model: krishmajumdar/arxiv-finetuned-v2
Author: krishmajumdar
Pipeline: sentence-similarity
Library: sentence-transformers
Tags: sentence-transformers, safetensors, bert, sentence-similarity, feature-extraction, dense, generated_from_trainer, dataset_size:614911, loss:MultipleNegativesRankingLoss, dataset_size:500, arxiv:1908.10084, arxiv:1705.00652, base_model:sentence-transformers/all-MiniLM-L6-v2, base_model:finetune:sentence-transformers/all-MiniLM-L6-v2, text-embeddings-inference, endpoints_compatible, region:us
Base models (finetune): id: sentence-transformers/all-MiniLM-L6-v2
Card metadata: tags: sentence-transformers, sentence-similarity, feature-extraction, dense, generated_from_trainer, dataset_size:614911, loss:MultipleNegativesRankingLoss, dataset_size:500
base_model: sentence-transformers/all-MiniLM-L6-v2
widget: source_sentence: <S> the generation of hydrodynamic radiation in interactions of pulsed proton and laser beams with matter is explored . </S> <S> the beams were directed into a water target and the resulting acoustic signals were recorded with pressure sensitive sensors . </S> <S> measurements were performed with varying pulse energies , sensor positions , beam diameters and temperatures . </S> <S> the obtained data are matched by simulation results based on the thermo - acoustic model with uncertainties at a level of 10@xmath0 . </S> <S> the results imply that the primary mechanism for sound generation by the energy deposition of particles propagating in water is the local heating of the medium . </S> <S> the heating results in a fast expansion or contraction and a pressure pulse of bipolar shape is emitted into the surrounding medium . </S> <S> an interesting , widely discussed application of this effect could be the detection of ultra - high energetic cosmic neutrinos in future large - scale acoustic neutrino detectors . </S> <S> for this application a validation of the sound generation mechanism to high accuracy , as achieved with the experiments discussed in this article , is of high importance .    </S> <S> cosmic neutrinos , acoustic neutrino detection , thermo - acoustic model , ultra - high energy cosmic rays , beam interaction </S>
sentences: in 1957 g.a . askaryan pointed out that ionisation and cavitation along a track of an ionising particle through a liquid leads to hydrodynamic radiation @xcite . in the 1960s , 1970s and 1980s , theoretical and experimental studies have been performed on the hydrodynamic radiation of beams and particles traversing dense media @xcite . the interest in characterising the properties of the acoustic radiation was , among other reasons , lead by the idea that the effect can be utilised to detect ultra - high energy ( @xmath1 ) cosmic , i.e. astrophysical neutrinos , in dense media like water , ice and salt . in the 1970s this idea was discussed within the dumand optical neutrino detector project @xcite and has been studied in connection with cherenkov neutrino detector projects since . the detection of such neutrinos is considerably more challenging than the search for high - energy neutrinos ( @xmath2 ) as currently pursued by under - ice and under - water cherenkov neutrino telescopes @xcite . due to the low expected fluxes , detector sizes exceeding 100km@xmath3 are needed @xcite . however , the properties of the acoustic method allow for sparsely instrumented arrays with @xmath4100 sensors / km@xmath3 . to study the feasibility of a detection method based on acoustic signals it is necessary to understand the properties of the sound generation by comparing measurements and simulations based on theoretical models . according to the so - called thermo - acoustic model @xcite , the energy deposition of particles traversing liquids leads to a local heating of the medium which can be regarded as instantaneous with respect to the hydrodynamic time scales . due to the temperature change the medium expands or contracts according to its bulk volume expansion coefficient @xmath5 . the accelerated motion, however that they are derived using the @xmath21 values determined for given @xmath62 and @xmath63 and hence do not account for the additional uncertainty introduced by allowed variations in these parameters ( which could affect the power spectrum normalization amplitude by as much as @xmath105 ) . from fig . 23(e ) , and given the uncertainties , we see that the fitting formulae of eqs . ( 8) and ( 9 ) provide an adequate summary for all the open - bubble inflation model spectra . the extreme @xmath106-@xmath80 @xmath58 normalization factor ( eq . [ 2 ] and table 8) for the flat - space scale - invariant spectrum open model ( w83 ) may be summarized by , for the lower 2-@xmath80 limit , @xmath107 , \eqno(10)\ ] ] and for the upper 2-@xmath80 limit , @xmath108 . \eqno(11)\ ] ] these fits are good to better than @xmath88 for @xmath109 ; again , they are derived from @xmath21 values determined at given @xmath62 and @xmath63 . given the uncertainties involved in the normalization procedure ( born of both statistical and other arguments ) it is not yet possible to quote a unique dmr normalization amplitude ( g96 ) . as a central " value for the @xmath58 normalization factor , we currently advocate the mean of eqs . ( 8) and ( 9 ) or eqs . ( 10 ) and ( 11 ) as required . we emphasize , however , that it is incorrect to draw conclusions about model viability based solely on this central " value . in conjunction with numerically determined transfer functions , the fits of eqs . ( 8)(11 ) allow for a determination of @xmath26 $ ] , accurate to a few percent . here the mean square linear, accordingly , the mean fluctuation value is not following a solution to the background equations of motion . evolution equations for the variance @xmath80 and skew @xmath42 are obtained after enforcing @xmath106 , yielding @xmath107 in both equations , the first term on the right - hand sides describes how @xmath81 and @xmath42 scale as the density function expands or contracts in response to the velocity field . these terms force @xmath80 and @xmath42 to scale in proportion to the velocity field . specifically , if we temporarily drop the second terms in each equation above , one finds that @xmath108 and @xmath109 . this precisely matches our expectation for the scaling of these quantities . hence , these terms account for the jacobians associated with infinitesimal transformations induced by the flow @xmath93 . for applications to inflationary non - gaussianity , the second terms in and are more relevant . these terms describe how each moment is sourced by higher moments and the interaction of the density function with the velocity field . in the example above , if we are in a situation where @xmath105 , the tails of the density function are moving faster than the core . this means that one tail is shrinking and the other is extending , skewing the probability density . the opposite occurs when @xmath110 . these effects are measured by the second term in . hence , by expanding our pdf to the third moment , and our velocity field to quadratic order , we are able to construct a set of evolution equations which include the leading - order source terms for each moment . there is little conceptually new as we move from one field to two . the new features are mostly technical in nature . our, source_sentence: <S> we study equilibrium configurations of swarming biological organisms subject to exogenous and pairwise endogenous forces . beginning with a discrete dynamical model </S> <S> , we derive a variational description of the corresponding continuum population density . </S> <S> equilibrium solutions are extrema of an energy functional , and satisfy a fredholm integral equation . </S> <S> we find conditions for the extrema to be local minimizers , global minimizers , and minimizers with respect to infinitesimal lagrangian displacements of mass . </S> <S> in one spatial dimension , for a variety of exogenous forces , endogenous forces , and domain configurations , we find exact analytical expressions for the equilibria . </S> <S> these agree closely with numerical simulations of the underlying discrete model.the exact solutions provide a sampling of the wide variety of equilibrium configurations possible within our general swarm modeling framework . </S> <S> the equilibria typically are compactly supported and may contain @xmath0-concentrations or jump discontinuities at the edge of the support . </S> <S> we apply our methods to a model of locust swarms , which are observed in nature to consist of a concentrated population on the ground separated from an airborne group . </S> <S> our model can reproduce this configuration ; quasi - two - dimensionality of the model plays a critical role .    swarm , equilibrium , aggregation , integrodifferential equation , variational model , energy , minimizer , locust </S>
sentences: integral equation ( [ eq : fie ] ) to find candidate solutions . then , we compute @xmath82 to determine whether @xmath59 is a local minimizer . finally , when possible , we show the positivity of @xmath67 to guarantee that @xmath59 is a global minimizer . as the continuum limit replaces individual particles with a density , we need to make sure the continuum problem inherits a physical interpretation for the underlying problem . if we think about perturbing an equilibrium configuration , we note that mass can not `` tunnel '' between disjoint components of the solution . as such we define the concept of a multi - component swarm equilibrium . suppose the swarm s support can be divided into a set of @xmath24 disjoint , closed , connected components @xmath91 , that is @xmath92 we define a swarm equilibrium as a configuration in which each individual swarm component is in equilibrium , @xmath93 we can still define @xmath82 in @xmath39 @xmath94 + f(x ) = \int_{{\omega_{{{\bar \rho}}}}}q(x - y ) { { \bar \rho}}(y)~dy + f(x),\ ] ] but now @xmath95 in @xmath96 . we can now define a swarm minimizer . we say a swarm equilibrium is a swarm minimizer if @xmath97 for some neighborhood of each component @xmath96 of the swarm . in practice this means that the swarm is an energy minimizer for infinitesimal redistributions of mass in the neighborhood of each component . this might also be called a lagrangian minimizer in the sense that the equilibrium is a minimizer with respect to infinitesimal lagrangian deformations of the distributions . it is crucial to note that even if a solution @xmath59 is a global minimizer , other multi - component swarm minimizers may still exist . these solutions are local minimizers, paper @xcite . in section [ sec2 ] we define precisely the model of interest and state our main results concerning the asymptotic behavior of the corresponding measure on spin and salt configurations with fixed concentration of salt . along with the results comes a description of the phase diagram and a discussion of freezing - point depression , phase separation , etc . , see section [ sec2.3 ] . our main results are proved in section [ sec3 ] . in @xcite we investigate the asymptotic of infinitesimal salt concentrations . interestingly , we find that , in order to induce phase separation , the concentration has to scale at least as the inverse linear size of the system . with the ( formal ) hamiltonian in mind , we can now start on developing the _ mathematical _ layout of the problem . to define the model , we will need to restrict attention to finite subsets of the lattice . we will mostly focus on rectangular boxes @xmath62 of @xmath63 sites centered at the origin . our convention for the boundary , @xmath64 , of the set @xmath65 will be the collection of sites outside @xmath66 with a neighbor inside @xmath66 . for each @xmath67 , we have the water and salt variables , @xmath68 and @xmath17 . on the boundary , we will consider fixed configurations @xmath69 ; most of the time we will be discussing the cases @xmath70 or @xmath71 , referred to as plus and minus boundary conditions . since there is no salt - salt interaction , we may as well set @xmath72 for all @xmath73 . we will start by defining the interaction hamiltonian . let @xmath65 be a finite set . for a spin configuration @xmath69 and the pair @xmath74, are hybridized with a taylort3 post - newtonian ( pn ) waveform as described in @xcite at matching frequencies @xmath30 and @xmath31 for mass - ratios @xmath32 and @xmath33 , respectively . taylort4 at 3.5pn order is known to match nr simulations exceedingly well for equal - mass , zero - spin bbh systems @xcite ( see also fig . 9 of @xcite ) . for @xmath34 , a taylort3 hybrid is very similar to a taylort4 hybrid , cf.figure 12 of @xcite . the mismatch between taylort3 and taylort4 hybrids is below @xmath35 at @xmath36 , dropping to below @xmath37 for @xmath38 , and @xmath39 for @xmath40 . these mismatches are significantly smaller than mismatches arising in the study presented here , so we conclude that our results are not influenced by the accuracy of the utilized @xmath28 pn - nr hybrid waveform . for higher mass - ratios , the pn - nr hybrids have a larger error due to the post - newtonian waveform @xcite . the error - bound on the hybrids increases with mass - ratio , however , is mitigated in our study here , because we use the @xmath41 hybrids only for total mass of @xmath42 , where less of the post - newtonian waveform is in band . because nr simulations are not available for arbitrary mass ratios , we will primarily concentrate our investigation to the equal - mass and zero - spin nr hybrid waveforms described above . the full imr waveform can be generated at any point along the @xmath43 line through a simple rescaling of amplitude and phase with total mass @xmath44 of the system . despite such a simple rescaling , the @xmath43 line lies orthogonal to lines of constant chirp mass @xcite , therefore tracing a, source_sentence: <S> we report on strong enhancement of mid - infrared second harmonic generation ( shg ) from sic nanopillars due to the resonant excitation of localized surface phonon - polaritons within the reststrahlen band . </S> <S> the magnitude of the shg peak at the monopole mode experiences a strong dependence on the resonant frequency beyond that described by the field localization degree and the dispersion of linear and nonlinear - optical sic properties . comparing the results for the identical nanostructures made of 4h and 6h sic polytypes </S> <S> , we demonstrate the interplay of localized surface phonon polaritons with zone - folded weak phonon modes of the anisotropic crystal . tuning the monopole mode in and out of the region where the zone - folded phonon is excited in 6h - sic , we observe a prominent increase of the already monopole - enhanced shg output when </S> <S> the two modes are coupled . envisioning this interplay as one of the showcase features of mid - infrared nonlinear nanophononics , we discuss its prospects for the effective engineering of nonlinear - optical materials with desired properties in the infrared spectral range .    </S> <S> light localization in sub - wavelength volumes is a core of modern nanophotonics . </S> <S> conventional methods of achieving strong confinement of the electromagnetic fields extensively utilize unique properties of surface plasmons . </S> <S> a remarkable variety of objects and materials supporting these excitations ensures the key role of plasmonics in a broad range of applications @xcite . </S> <S> apart from unparalleled sensitivity of plasmonic structures to the optical properties of the environment , strong light localization facilitates nonlinear - optical effects @xcite . </S> <S> owing to the spectral tunability of the localized plasmon resonances and their sizeable nonlinearity , metallic nanostructures of different shapes and sizes have earned their place in nonlinear photonics .    despite obvious advantages of plasmon - based nanophotonics , metallic nanoobjects exhibit significant optical losses , which lower the quality factor of the localized surface plasmon modes . </S> <S> fast plasmon damping ( typically on the order of 10 fs ) due to ohmic losses @xcite thus inhibits nonlinear - optical conversion . </S> <S> an alternative , promising metal - free approach has been suggested , utilizing polar dielectrics such as sic @xcite or bn @xcite for high - quality light confinement in the mid - infrared ( ir ) . in these materials , </S> <S> the subdiffractional confinement of electromagnetic radiation relies upon surface phonon polaritons ( sphp ) in the reststrahlen band : the electric polarization is created due to coherent oscillations of the ions instead of the electron or hole densities . due to the significantly longer scattering times associated with optical phonons </S> <S> as compared to surface plasmons , the lifetimes of sphps tend to be on the order of picoseconds , much longer than their plasmonic counterparts @xcite . </S> <S> in addition , due to energies associated with optical phonons , sphps with typical frequencies within the mid - ir ( @xmath0 ) to the thz domain hold high promise for spectroscopic and nanophotonic applications @xcite .    in this letter </S> <S> , we undertake a first step towards the largely unexplored domain of mid - ir nonlinear nanophononics . </S> <S> we study the nonlinear - optical response of localized sphps using nanostructures made of different polytypes of sic . using free electron laser ( fel ) radiation in the mid - ir spectral range @xcite </S> <S> , we probe second harmonic generation from rectangular arrays of sub - diffractional , cylindrical sic nanopillars . </S> <S> the shg yield in the reststrahlen band of sic demonstrates prominent enhancement at the wavelengths associated with the excitation of the sphp eigenmodes of the pillars . depending on both the size and the spatial periodicity of the pillars , </S> <S> the shg - probed eigenmode exhibits a spectral shift accompanied with strong variations of the shg intensity . analyzing different sic polytypes </S> <S> , we demonstrate the interplay of the localized sphps with the zone - folded optical phonon modes . </S> <S> we further conclude that strong coupling of the two modes allows for a significant additional modulation of the sphp - enhanced shg output .        </S> <S> the schematic of our experimental approach is outlined in fig .  </S> <S> [ general],a . </S> <S> we employed a non - collinear shg configuration discussed elsewhere @xcite to perform spectroscopic shg measurements on square arrays of 1  @xmath1m - tall 4h - sic and 6h - sic pillars with the main axis of the arrays in the _ xz _ plane of incidence . </S> <S> the fundamental radiation incident at 28 and 62 degrees with respect to the normal to the sample surface was focused onto the sample with a peak fluence on the order of 10 mj/@xmath2 . </S> <S> both 4h and 6h - sic samples were c - cut so that the _ c_-axis of the crystals was parallel to the surface normal . </S> <S> typical shg and linear reflectivity spectra collected using the fel radiation for the two incident polarisations are presented in fig .  </S> <S> [ general],b - e . </S> <S> there , the respective spectra of the bare substrate are shown for comparison . </S> <S> for _ p_-polarised fundamental radiation ( fig .  </S> <S> [ general],d ) , the shg response features two pronounced peaks located at the zone - center frequencies of transverse and longitudinal optical phonons in sic @xcite , around 797 @xmath3 and 965 @xmath3 , respectively . the corresponding shg spectrum from the nanopillars demonstrate a much stronger shg signal at around 900 @xmath3 . due to the absence of this peak in the shg spectrum </S> <S> when the fundamental radiation is _ </S> <S> s_-polarised , we attribute this shg feature to the excitation of the monopole sphp mode in the nanopillars @xcite .    in general , </S> <S> the outgoing shg field @xmath4 is related to the incident electromagnetic fields @xmath5 via the so - called local field factors @xmath6 :    @xmath7    where @xmath8 is the nonlinear polarisation and @xmath9 is the nonlinear susceptibility tensor . </S> <S> the excitation of the sphp monopole mode leads to strong localization of the _ z_-projection of the fundamental electric field @xmath10 ( normal to the surface plane ) and thus a resonant enhancement of @xmath11 . </S> <S> the latter results in a pronounced increase of the shg output when the fundamental radiation is _ p_-polarised . </S> <S> however , the sphp dipole modes observed in the range of 920960  @xmath3 rely on the resonant enhancement of the in - plane electric fields described by the local field factors @xmath12 and thus can be excited with both _ </S> <S> p_- and _ s_-polarised fundamental radiation . </S> <S> the total shg response is given by a vector sum of the terms on the right hand side of eq .  </S> <S> ( 1 ) originating from various tensor components of the nonlinear susceptibility @xmath13 . </S> <S> as the strength of @xmath14 is the largest in this spectral range @xcite , the sphp monopole mode , with an enhancement of @xmath11 , naturally results in a higher shg output than the dipole modes .    </S> <S> the results of the systematic studies of the shg response of various arrays of nanopillars are summarized in fig .  </S> <S> [ shifts ] for the 4h - sic ( a , c ) and 6h - sic ( b , d ) samples . </S> <S> the panels ( a - b ) illustrate the evolution of the shg spectra upon varying pillar diameter @xmath15 . </S> <S> it is seen that upon decreasing @xmath15 , the sphp monopole - driven shg peak exhibits a clear redshift . </S> <S> remarkably , while the sphp monopole mode shifts in the range of about 890 - 910 @xmath3 , the shg enhancement factor associated with the excitation of the sphp monopole mode varies strongly with @xmath15 . </S> <S> the panels ( c - d ) offer a zoom - in into the evolution of the sphp monopole mode - driven shg for a large variety of nanopillar arrays , indicating that the variations of the shg enhancement are observed for both 4h and 6h samples . </S> <S> the dependences of the sphp monopole - driven shg output on the spectral position of the sphp monopole mode for the two sic polytypes are shown in fig .  </S> <S> [ analysis],a with open symbols .     </S> <S> = 1200 , 1100 and 1000 nm , respectively . </S> <S> , scaledwidth=47.0% ]        the strong dispersion in the sic reststrahlen band suggests that the observed spectral dependence of the shg enhancement could be captured in numerical simulations . </S> <S> we calculated shg response using both linear and nonlinear sic dispersion@xcite , the results of the simulation of the linear optical response@xcite , and nonlinear polarization @xmath16 from eq .  </S> <S> ( 1 ) spatially integrated over the sic volume , with the following non - zero components of the nonlinear susceptibility : @xmath14 , @xmath17 and @xmath18 . </S> <S> the resultant shg spectra simulated with comsol multiphysics software ( www.comsol.com ) are shown in fig .  </S> <S> [ analysis],b with full symbols . </S> <S> it is seen that the steep experimental dependence can not be quantitatively described within the simple model used in the calculations , which yields only a moderate increase of the shg output when the sphp monopole mode frequency is decreased .    </S> <S> we note the work of carpetti _ </S> <S> et al_. @xcite where the authors thoroughly examined plasmon - induced shg enhancement from arrays of au nanoparticles as a function of the inter - particle distance @xmath19 . in the regime of @xmath20 ( as it is in our case ) , the dependence of the shg output on @xmath19 was explained in terms of the changing filling factor ( and thus the associated number of active nanoemitters ) . </S> <S> for very small inter - particle gaps ( @xmath21 ) , a modulation of the shg output has been attributed to the modification of the electromagnetic field localization in the gaps @xcite . </S> <S> further , a large mismatch between the spatial period of the nanopillars @xmath22 and the resonant light wavelength @xmath23 rules out the excitation of propagating surface polaritons @xcite which are known to enhance the shg output @xcite . </S> <S> since all these effects are included in our simulations , we conclude that the origin of the observed shg enhancement is unrelated to the periodicity of the array .    </S> <S> an alternative scenario for the observed trend could invoke modifications of the non - local shg contribution enhanced by a regular array structure . </S> <S> the importance of the non - local shg was already demonstrated in a number of subwavelength - separated plasmonic nanoobjects @xcite . </S> <S> the amplitude and phase of this non - local shg source depends on the electric field distribution , i.e. on both the pillar size @xmath15 and the periodicity @xmath24 . </S> <S> as such , the interference conditions between the shg sources vary for different samples , thus resulting in a strong modification of the shg output .    </S> <S> further , the apparent difference in the shape of the resonant shg output for the 4h and 6h samples ( see fig .  [ shifts ] ) is related to the anisotropic nature of sic . </S> <S> the hexagonal sic polytypes are known to exhibit zone - folded weak modes in the reststrahlen region @xcite originating from particular stacking of the atomic layers along the _ </S> <S> c_-axis of the crystal @xcite . </S> <S> these weakly ir - active zone - folded modes can be visualised in the reflectivity measurements at oblique incidence @xcite . </S> <S> although zone - folded modes exist in both 4h and 6h polytypes , different stacking of the sic atomic layers is responsible for them having different frequencies , as illustrated in fig .  </S> <S> [ analysis],c - d . </S> <S> the additional periodicity in the crystal results in folding of the large brillouin zone thus modifying the phonon dispersion and making the excitation of phonons with non - zero wavevectors ( @xmath25 ) possible . </S> <S> it is seen in fig .  </S> <S> [ analysis],d that the zone - folded mode in the 6h - sic polytype with the reduced wavevector @xmath26 @xmath27 can be excited in the range of @xmath28  @xmath3 which is close to the typical monopole sphp resonant frequency of the sic nanopillars discussed above . </S> <S> in particular , the interaction of the sphp and zone - folded mode which shifted the apparent spectral positions of the monopole sphp eigenmode in the linear response @xcite , is seen responsible for the complex structure of the resonant shg output in our experiments ( fig .  </S> <S> [ shifts],d ) . </S> <S> the weak ir activity of the zone - folded modes is related to the large negative dielectric permittivity of sic in the reststrahlen band . as such , the out - of - plane component of the electromagnetic field @xmath10 remains small which inhibits the coupling of incident light to the zone - folded phonon mode . </S> <S> however , the excitation of the sphp monopole mode in the nanopillars drives a strong increase of @xmath10 , which facilitates the sphp monopole interaction with the zone - folded phonon ( fig .  </S> <S> [ analysis],c ) .    </S> <S> figure  [ analysis],a illustrates the effect of the zone - folded mode on the observed shg output . </S> <S> the open red squares ( 4h ) and blue circles ( 6h ) depict the shg intensity obtained at the sphp monopole ( resonant ) frequencies , and the dashed lines illustrate a clear correlation between the maximum shg output and the spectral position of the sphp monopole peak . </S> <S> similar trends are observed for the 4h and 6h - sic samples as long as the sphp monopole and the zone - folded mode are well - separated . </S> <S> when these two resonances start to overlap , an additional enhancement of the shg output produced at the sphp monopole resonance in 6h - sic samples is observed . </S> <S> moreover , the dependence of the shg signal at the frequency of the zone - folded mode @xmath29  @xmath3 ( green triangles ) exhibits a much faster increase when the two resonances are brought together ( dotted line ) , indicating an efficient interplay between the sphp monopole and the zone - folded mode .    </S> <S> we note that the interaction of the localized sphp eigenmodes and the intrinsic excitations of the medium is a unique fingerprint of mid - ir nanophononics . indeed </S> <S> , surface plasmon excitations in metals rely on the free electron gas , which is essentially isotropic . as such , the shg output of plasmonic nanostructures is ( i ) largely determined by the metal of choice , usually au , ( ii ) exhibits only weak spectral dependence @xcite and ( iii ) is limited by robust phase relations in the likely case of multiple shg sources @xcite . on the contrary , the flexibility of the sphps is provided by the coupling of the surface phonon polariton excitations to the intrinsic bulk phonon modes . the latter can be engineered by designing artificial metamaterials based on hybrid multilayer structures @xcite , thus allowing for an effective control of their optical properties . to summarize , </S> <S> we have observed shg output enhancement associated with the excitation of the sphp eigenmodes in an array of nanopillars grown from sic of different polytypes . </S> <S> the strongest shg output is associated with the excitation of the monopole sphp mode characterized by strong localization of the normal to surface projection of the electric field @xmath10 . </S> <S> the spectral positions of the shg peaks shift according to the geometric parameters of the nanophononic structures . </S> <S> we found a strong dependence of the magnitude of the shg enhancement on the resonant frequency . </S> <S> this experimentally observed dependence can not be quantitatively described by simply taking into account the sub - diffractional field localization and the dispersion of the linear and nonlinear optical properties of sic . </S> <S> further , we discuss the interplay of the sphps and the intrinsic crystalline anisotropy for an efficient nonlinear - optical conversion . this mechanism is supported by the shg spectral measurements on the 6h - sic nanopillars where excitation of the sphp monopole mode interacting with the weak zone - folded phonon resulted in an additional enhancement of the shg output . </S> <S> the presence of intrinsic resonances strongly alters the phase relations in their vicinity , providing a natural way for optimizing the shg response in a relatively narrow spectral range . </S> <S> our findings demonstrate high potential of mid - ir nonlinear nanophononics as a novel and promising platform for nonlinear optics and illustrate the rich opportunities it provides for efficient control over nonlinear - optical response .    </S> <S> the authors thank g.  kichin and a.  kirilyuk ( radboud university nijmegen ) for stimulating discussions . </S> <S> s.a.m . acknowledges the office of naval research , the royal society , and the lee - lucas chair in physics . a.j.g . acknowledges financial support from the nrc / nrl postdoctoral fellowship program . </S> <S> funding for j.d.c . was provided by the office of naval research through the naval research laboratory s nanoscience institute . </S>
sentences: interpreted as the sum of @xmath360 over the relevant ( discrete ) values of @xmath45 and @xmath115 . let @xmath361 denote the sum of @xmath362 over all @xmath363 and @xmath364 for which @xmath365 and @xmath366 are integers and @xmath367 and @xmath368 . ( this is exactly the set of magnetizations and spin - salt overlaps contributing to the set @xmath369 . ) applying to extract the exponential behavior of the last probability in , and using to do the same for the quantity @xmath355 , we get @xmath370 where @xmath247 is as in . as a consequence of the above estimate we have @xmath371 for any @xmath112 and any @xmath372 . next we will attend to the denominator in . pick @xmath373 and consider the set latexmath:[\[{\mathcal m}_\delta=\bigl\{(m,\theta)\colon write @xmath359 as a sum of two terms , @xmath375 , with @xmath376 obtained by summing @xmath377 over the admissible @xmath378 and @xmath379 collecting the remaining terms . by lemma [ lemma3.5 ] we know that @xmath380 decays exponentially in @xmath238 and so the decisive contribution to @xmath359 comes from @xmath376 . assuming that @xmath381 , let us cover @xmath382 by finite number of sets of the form @xmath383\times[\theta_\ell'-\epsilon,\theta_\ell'+\epsilon]$ ] , where @xmath384 and @xmath385 are such that @xmath386 and @xmath387 are integers . then @xmath376 can be bounded as in @xmath388 moreover , the right - hand side is bounded by the left - hand side times a polynomial in @xmath32 . taking logarithms , dividing by @xmath238 , taking the limit @xmath295 , refining the cover and applying the continuity of @xmath389 allows us to conclude that @xmath390}{\mathscr{g}}_{h , c}(m,\theta).\ ] ] combining these observations , is proved . proof of theorem [ thm1 ] the conclusion follows from by similar arguments that prove . the only remaining thing to, on the mass ratio @xmath6 , which is not captured by the low order perturbation theory . a second common approach was developed by elkomoss and munchy,@xcite and uses an effective exciton - exciton potential defined by @xmath28 , where @xmath29 is the wavefunction for two free excitons a distance @xmath30 apart . the effective potential @xmath31 arises from the hartree term and is used in a two - particle central - field calculation . while an exciton - exciton scattering pseudo - potential would be a very useful tool , this approximate form has some serious drawbacks . among its deficiencies are a lack of correlation , no van der waals attraction , a failure to reproduce biexciton states , and a vanishing interaction potential for @xmath32 . the cross sections calculated by this method are small and lack qualitative agreement with the results of the present work . some insight into exciton - exciton scattering can be gained by considering the bound states , biexcitons . since the number of bound states , @xmath33 , enters in the phase shift at zero energy , @xmath34 , it is necessary that a good computation method for low energy scattering be able accurately calculate biexciton binding energies.@xcite for the mass ratios considered ( and far beyond , including deuterium ) the biexcitons can not bind in the @xmath19 states , so biexcitons in rotational @xmath35 states always have @xmath18 wavefunctions . detailed theoretical descriptions of biexcitons can be found in ref . the equal mass case was shown to have a bound biexciton by hyllerass and ore using a variational argument,@xcite and a better variational estimate of the binding energy was given by brinkman , rice and bell,@xcite who found @xmath36 , where @xmath37 is the exciton binding energy ., 159162 , b. ; korobkin , d. ; fietz , c. ; carole , d. ; ferro , g. ; shvets , g. critically coupled surface phonon - polariton excitation in silicon carbide . expr . _ * 2007 * , _ 34 _ , 26672669 caldwell , j. d. ; glembocki , o. j. ; francescato , y. ; sharac , n. ; giannini , v. ; bezares , f. j. ; long , j. p. ; owrutsky , j. c. ; vurgaftman , i. ; tischler , j. g. ; wheeler , v. d. ; bassim , n. d. ; shirey , l. m. ; kasica , r. ; maier , s. a. low - loss , extreme subdiffraction photon confinement via silicon carbide localized surface phonon polariton resonators . _ nano lett . _ * 2013 * , _ 13 _ , 36903697 chen , y. ; francescato , y. ; caldwell , j. d. ; giannini , v. ; ma , t. w. w. ; glembocki , o. j. ; bezares , f. j. ; taubner , t. ; kasica , r. ; hong , m. ; maier , s. a. spectral tuning of localized surface phonon polariton resonators for low - loss mid - ir applications . _ acs photonics _ * 2014 * , _ 1 _ , 718724 caldwell , j. d. ; kretinin , a. v. ; chen , y. ; giannini , v. ; fogler , m. m. ; francescato , y. ; ellis , c. t. ; tischler , j. g. ; woods , c. r. ; giles , a. j. ; hong , m. ; watanabe , k. ; taniguchi , t. ; maier , s. a. ; novoselov , k. s. sub - diffractional volume - confined polaritons, source_sentence: <S> in 84 , 258 ( 2000 ) , mateos conjectured that current reversal in a classical deterministic ratchet is associated with bifurcations from chaotic to periodic regimes . </S> <S> this is based on the comparison of the current and the bifurcation diagram as a function of a given parameter for a periodic asymmetric potential . </S> <S> barbi and salerno , in 62 , 1988 ( 2000 ) , have further investigated this claim and argue that , contrary to mateos claim , current reversals can occur also in the absence of bifurcations . </S> <S> barbi and salerno s studies are based on the dynamics of one particle rather than the statistical mechanics of an ensemble of particles moving in the chaotic system . </S> <S> the behavior of ensembles can be quite different , depending upon their characteristics , which leaves their results open to question . in this paper we present results from studies showing how the current depends on the details of the ensemble </S> <S> used to generate it , as well as conditions for convergent behavior ( that is , independent of the details of the ensemble ) . </S> <S> we are then able to present the converged current as a function of parameters , in the same system as mateos as well as barbi and salerno . </S> <S> we show evidence for current reversal without bifurcation , as well as bifurcation without current reversal . </S> <S> we conjecture that it is appropriate to correlate abrupt changes in the current with bifurcation , rather than current reversals , and show numerical evidence for our claims . </S>
sentences: of this . however , not all spikes or jumps correspond to a bifurcation , nor vice versa . the open question is clearly to figure out if the reason for when these rules are violated or are valid can be made more concrete . a.k . gratefully acknowledges t. barsch and kamal p. singh for stimulating discussions , the reimar lst grant and financial support from the alexander von humboldt foundation in bonn . a.k.p . is grateful to carleton college for the ` sit , wallin , and class of 1949 ' sabbatical fellowships , and to the mpipks for hosting him for a sabbatical visit , which led to this collaboration . useful discussions with j .- m . rost on preliminary results are also acknowledged . p. hnggi and bartussek , in nonlinear physics of complex systems , lecture notes in physics vol . 476 , edited by j. parisi , s.c . mueller , and w. zimmermann ( springer verlag , berlin , 1996 ) , pp.294 - 308 ; r.d . asturmian , science * 276 * , 917 ( 1997 ) ; f. jlicher , a. ajdari , and j. prost , rev . mod . phys . * 69 * , 1269 ( 1997 ) ; c. dring , nuovo cimento d*17 * , 685 ( 1995 ) s. flach , o. yevtushenko , and y. zolotaryuk , phys . rev . lett . * 84 * , 2358 ( 2000 ) ; o. yevtushenko , s. flach , y. zolotaryuk , and a. a. ovchinnikov , europhys . lett . * 54 * , 141 ( 2001 ) ; s. denisov et al . e * 66 * , 041104 ( 2002 ), two - folds . for major stations , we have the total number of passengers that crossed the boom gates , in and out . for stations without boom gates , the observations have to estimated using a survey . we also have access to the total number of people with a valid zone ticket at time @xmath1 ( e.g. the day of the analysis ) , denoted @xmath13 , @xmath14 in the end , the total number of regular passenger at the time period @xmath1 will be denoted @xmath15 , and we have , @xmath16 with these very different observations , we need a good fitting model based on reasonable assumptions . sections [ mam - gm ] , [ mam - cm ] , [ mam - da ] and [ mam - rm ] presents these assumptions for each parameter in our model . recall that @xmath17 is a matrix of count , the main assumption on that matrix is that the number of passenger is the sum of the casual passengers ( @xmath18 ) plus the regular passengers ( @xmath15 ) plus a matrix stating the unusual big events such as major sporting events , or large concerts ( called @xmath19 ) , @xmath20 the casual commuter journey could be assumed to be poisson distributed i.e. @xmath21 is supposed to be drawn with a poisson distribution which parameter belong to the matrix @xmath22 . ] where @xmath22 is the matrix of means for the counts . + however , the variance of the counts are not expected to be equal to their mean and so the poisson counts assumption may be unrealistic . therefore , we decided to use a negative binomial regression model for @xmath23 , which can be over - dispersed in order to, to compare against the `` correct '' answer . the natural extension of this work is to expand into higher dimensions where nr waveforms are available only at certain , discrete mass - ratios @xmath167 . in this section we consider expanding our approach of interpolating nr projection coefficients from a two - dimensional template bank containing unequal - mass waveforms . we compute a template bank of phenomb waveforms covering mass - ratios @xmath167 from 1 to 6 and total masses @xmath168 . this mass range is chosen to facilitate comparison with previous work done by @xcite . for the two - dimensional case the construction of a template bank is no longer as straightforward as before due to the additional degree of freedom associated with varying @xmath167 . one method that has been advanced for this purpose is to place templates hexagonally on the waveform manifold @xcite . using this procedure we find @xmath169 templates are required to satisfy a minimal match of 0.97 . following the waveform preparation of @xcite , templates are placed in the rows of a matrix @xmath87 with real and imaginary components filled in alternating fashion where the whitened waveforms are arranged in such a way that their peak amplitudes are aligned . the waveforms are sampled for a total duration of @xmath170 with uniform spacing @xmath9 so that @xmath171 of memory is required to store the contents of @xmath87 if double precision is desired . application of transforms the 16 complex - valued waveforms into 32 real - valued orthonormal basis waveforms . the aim is to sample the coefficients of nr waveforms projected onto the svd basis of phenomb waveforms using mass - ratios for which nr data exists , and then interpolate amongst these to construct a numerical waveform family, source_sentence: <S> the effect of a random phase diffuser on fluctuations of laser light ( scintillations ) is studied . </S> <S> not only spatial but also temporal phase variations introduced by the phase diffuser are analyzed . </S> <S> the explicit dependence of the scintillation index on finite - time phase variations is obtained for long propagation paths . </S> <S> it is shown that for large amplitudes of phase fluctuations , a finite - time effect decreases the ability of phase diffuser to suppress the scintillations . </S>
sentences: operators @xmath67 ( their dependence on time is as in vacuum ) . the term for @xmath68 can be obtained from eq . [ twelve ] by putting @xmath69 . substituting both distribution functions into eq . [ eight ] , we obtain @xmath70 @xmath71 @xmath72:\big>,\ ] ] where @xmath73 and @xmath74 are solutions of eqs . [ twelve ] with the initial conditions @xmath63 and @xmath75 , respectively . the operators on the right side of eq . [ thirteen ] are related through matching conditions with the amplitudes of the exiting laser radiation ( see ref . @xcite ) by the relation @xmath76 where @xmath77 is the operator of the laser field which is assumed to be a single - mode field and the subscript ( @xmath78 ) means perpendicular to the @xmath28-axis component . the function @xmath79 describes the profile of the laser mode , which is assumed to be gaussian - type function [ @xmath80 . @xmath1 desribes the initial radius of the beam . to account for the effect of the phase diffuser , a factor @xmath81 or @xmath82 should be inserted into the integrand of eq . [ fourteen ] . the quantity @xmath83 is the random phase introduced by the phase diffuser . a similar consideration is applicable to each of four photon operators entering both terms in square brackets of eq . [ thirteen ] . it can be easily seen that the factor @xmath84},\ ] ] describing the effect of phase screen on the beam , enters implicitly the integrand of eq . [ thirteen ] ( the indices @xmath78 are omitted here for the sake of brevity ) . there are integrations over variables @xmath85 as shown in eq . [ fourteen ] . furthermore , the brackets @xmath16 ,, curves in each panel , although in each panel two of them almost overlap . solid , dotted , and dashed lines show the open - bubble inflation cases , accounting only for the fluctuations generated during the evolution inside the bubble ( type [ 1 ] spectra , solid lines ) , also accounting for the fluctuations generated in the first epoch of spatially - flat inflation ( type [ 2 ] spectra , dotted lines these almost exactly overlap the solid lines ) , and finally also accounting for the fluctuations corresponding to the non - square - integrable basis function ( type [ 3 ] spectra , dashed lines ) . dot - dashed lines correspond to the flat - space scale - invariant spectrum open model ( type [ 4 ] spectra ) . these are for @xmath64 and @xmath270 . 17.marginal likelihood densities [ @xmath271 for @xmath1 , normalized to unity at the peak , for the open - bubble inflation model accounting only for fluctuations generated during the evolution inside the bubble ( rp94 ) , for the eight different dmr data sets , and for @xmath121 gyr , @xmath8 . panel ( a ) is from the ecliptic - frame analyses , and panel ( b ) is from the galactic - frame analyses . two of the four lines in each panel are from the analysis without the faint high - latitude foreground galactic emission correction , either accounting for ( dot - dashed lines ) or ignoring ( solid lines ) the quadrupole moment . the other two lines in each panel are from the analysis with this galactic emission correction , either accounting for ( dotted lines ) or ignoring ( dashed lines ) the quadrupole moment . 19.marginal likelihood, that the candidate is detected with s / n @xmath136 in the unaffected image and also s / n @xmath137 in the image affected by the bad pixel . hence , we are confident that the source is real and that the photometry from the final drizzled image is robust . the sixth and final candidate is confidently detected at s / n@xmath138 in @xmath46 ( @xmath120 ) , and also in the @xmath38 with s / n = 3.7 . its photometric redshift is sharply peaked at @xmath139 , with a secondary solution at @xmath140 . this candidate is also very compact , with measured half - light radius @xmath141 , and the highest stellarity of the sample ( class_star = 0.91 ) . combining compactness with high stellarity from a high s / n source , a stellar nature ( cool dwarf ) for this source is relatively likely , as we discuss in section [ contamination ] . to translate the results on the search of possible candidates at @xmath3 from the archival borg[z8 ] data into a number density / luminosity function determination , we need to assess both the impact of contamination in our sample , and the effective volume probed by the data . there are multiple classes of lower-@xmath24 sources that may have similar @xmath103 colors to @xmath19 lyman - break galaxies ( lbgs ) , such as galactic stars , intermediate - redshift passive galaxies , and strong line emitters . cool , red stars in the milky way may be possible contaminants of our sample , although typical colors lack a strong @xmath103 drop . at low signal - to - noise ratio , the separation of point - like galactic stars from resolved galaxies using the ` sextractor ` class_star
pipeline_tag: sentence-similarity
library_name: sentence-transformers
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