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Special Issue "BGL2017: 10th Bolyai-Gauss-Lobachevsky Conference on Non-Euclidean Geometry and Its Applications"

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Special Issue Information
Published Papers

A special issue of Universe (ISSN 2218-1997).

Deadline for manuscript submissions: closed (31 October 2017) | Viewed by 63661

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Special Issue Editors

Prof. Dr. Máté Csanád

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Guest Editor

Department of Atomic Physics, Eötvös Loránd University, Pázmány P. s. 1/A, H-1117 Budapest, Hungary
Interests: hydrodynamics in high-energy heavy ion physics; Bose–Einstein correlations; femtoscopy; forward (small-x) processes in particle physics
Special Issues, Collections and Topics in MDPI journals

Prof. Dr. T. Csörgő, MAE

E-Mail Website
Guest Editor

Scientific Advisor, Wigner Research Centre for Physics, Budapest and Research Professor, MATE Institute of Technology KRC, Gyöngyös, Hungary
Interests: theoretical nuclear physics; experimental nuclear physics; theoretical particle physics; experimental particle physics
Special Issues, Collections and Topics in MDPI journals

Dr. Tamás Novák

E-Mail Website
Guest Editor

Department Head, Department of Applied Informatics, EKE KRC, H-3200 Gyöngyös, Mátrai út 36, Hungary
Interests: Bose-Einstein correlations; Lévy-stable distributions; financial mathematics; seismology for gravitational waves

Special Issue Information

Dear Colleagues,

This special issue is dedicated to the conference: 10th Bolyai-Gauss-Lobachevsky Conference on Non-Euclidean Geometry and Its Applications (BGL2017) https://indico.cern.ch/event/586799/overview.

Traditionally, the topics of the Bolyai Gaus Lobachevsky conference series covers the following three main areas:

Matematics: Non-Euclidean geometry and other topics related to Bolyai, Gauss and Lobachevsky (BGL)
Physics: Modern physics and the heritage of BGL
History of science: Recent results and the heritage of BGL
Science outreach

In 2017, we invite submissions of talks within the above main areas in general, and related to the following topics in particular:

Applications of non-Euclidean geometry in physics
Applications of non-Euclidean geometry in informatics and other fields of science
Biographies, bibliography, and personal relations of BGL
Diffraction at LHC, and optical methods in accelerator physics
Non-Gaussian Femtoscopy in high energy physics
New solutions of fireball hydrodynamics including Navier-Stokes
Gravitational waves and curved space-time
History of science, related to BGL
Metric theory, integrals in the Lobachevsky space
Recent results on absolute geometry in mathematics
Riemannian geometry, generalisations of the hyperbolic space
Science outreach - methods to spread and to popularize science
Other important new developments (open to suggestions).

Dr. Máté Csanád

Prof. Tamás Csörgő

Dr. Tamás Novák
Guest Editors

Manuscript Submission Information

Manuscripts should be submitted online at www.mdpi.com by registering and logging in to this website. Once you are registered, click here to go to the submission form. Manuscripts can be submitted until the deadline. All submissions that pass pre-check are peer-reviewed. Accepted papers will be published continuously in the journal (as soon as accepted) and will be listed together on the special issue website. Research articles, review articles as well as short communications are invited. For planned papers, a title and short abstract (about 100 words) can be sent to the Editorial Office for announcement on this website.

Submitted manuscripts should not have been published previously, nor be under consideration for publication elsewhere (except conference proceedings papers). All manuscripts are thoroughly refereed through a single-blind peer-review process. A guide for authors and other relevant information for submission of manuscripts is available on the Instructions for Authors page. Universe is an international peer-reviewed open access monthly journal published by MDPI.

Please visit the Instructions for Authors page before submitting a manuscript. Submitted papers should be well formatted and use good English. Authors may use MDPI's English editing service prior to publication or during author revisions.

Published Papers (26 papers)

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Open AccessFeature PaperEditor’s ChoiceArticle

New Exact Solutions of Relativistic Hydrodynamics for Longitudinally Expanding Fireballs

and

Universe 2018, 4(6), 69; https://doi.org/10.3390/universe4060069 - 01 Jun 2018

Cited by 15 | Viewed by 2547

Abstract

We present new, exact, finite solutions of relativistic hydrodynamics for longitudinally expanding fireballs for arbitrary constant value of the speed of sound. These new solutions generalize earlier, longitudinally finite, exact solutions, from an unrealistic to a reasonable equation of state, characterized by a temperature independent (average) value of the speed of sound. Observables such as the rapidity density and the pseudorapidity density are evaluated analytically, resulting in simple and easy to fit formulae that can be matched to the high energy proton–proton and heavy ion collision data at RHIC and LHC. In the longitudinally boost-invariant limit, these new solutions approach the Hwa–Bjorken solution and the corresponding rapidity distributions approach a rapidity plateaux. Full article

(This article belongs to the Special Issue BGL2017: 10th Bolyai-Gauss-Lobachevsky Conference on Non-Euclidean Geometry and Its Applications)

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Open AccessArticle

Scaling Properties of Spectra in New Exact Solutions of Rotating, Multi-Component Fireball Hydrodynamics

Tamás Csörgő

and

Gábor Kasza

Universe 2018, 4(4), 58; https://doi.org/10.3390/universe4040058 - 26 Mar 2018

Cited by 4 | Viewed by 2164

Abstract

We describe fireballs that rehadronize from a perfect fluid of quark matter, characterized by the lattice QCD equation of state, to a chemically frozen, multi-component mixture, that contains various kinds of observable hadrons. For simplicity and clarity, we apply a non-relativistic approximation to describe the kinematics of this expansion. Unexpectedly, we identify a secondary explosion that may characterize fireball hydrodynamics at the QCD critical point. After rehadronization, the multi-component mixture of hadrons keeps on rotating and expanding together, similarly to a single component fluid. After kinetic freeze-out, the effective temperature

T_{i}

of the single-particle spectra of hadron type

h_{i}

is found to be a sum of the kinetic freeze-out temperature

T_{f}

(that is independent of the hadron type

h_{i}

) and a term proportional to the mass

m_{i}

of hadron type

h_{i}

. The coefficient of proportionality to

m_{i}

is found to be independent of the hadron type

h_{i}

but to be dependent on the radial flow and vorticity of collective dynamics. Full article

(This article belongs to the Special Issue BGL2017: 10th Bolyai-Gauss-Lobachevsky Conference on Non-Euclidean Geometry and Its Applications)

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Open AccessArticle

PHENIX Results of Three-Particle Bose-Einstein Correlations in \({\sqrt{s_{NN}}}\) = 200 GeV Au+Au Collisions

Tamás Novák

Universe 2018, 4(3), 57; https://doi.org/10.3390/universe4030057 - 19 Mar 2018

Cited by 2 | Viewed by 2041

Abstract

Bose-Einstein correlations (BECs) of identical hadrons reveal information about hadron creation from the strongly interacting matter formed in ultrarelativistic heavy-ion collisions. The measurement of three-particle correlations may in particular shed light on hadron creation mechanisms beyond thermal/chaotic emission. In this paper, we show the status of PHENIX measurements of three-pion correlations as a function of momentum differences within the triplets. We analyze the shape of the correlation functions through the assumption of Lévy sources and a proper treatment of the Coulomb interaction within the triplets. We measure the three-particle correlation strength (

λ_{3}

), which, together with the two-particle correlation strength

λ_{2}

, encodes information about hadron creation mechanisms. From a consistent analysis of two- and three-particle correlation strengths, we establish a new experimental measure of thermalization and coherence in the source. Full article

(This article belongs to the Special Issue BGL2017: 10th Bolyai-Gauss-Lobachevsky Conference on Non-Euclidean Geometry and Its Applications)

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Open AccessEditor’s ChoiceArticle

Investigating the Poor Match among Different Precessing Gravitational Waveforms

and

Universe 2018, 4(3), 56; https://doi.org/10.3390/universe4030056 - 16 Mar 2018

Viewed by 2255

Abstract

The sixfold direct detection of gravitational waves opened the era of gravitational wave astronomy. All of these gravitational waves were emitted by black hole or neutron star binaries. The determination of the parameters characterizing compact binaries requires the accurate knowledge of waveforms. Three different waveforms (Spin Dominated, SpinTaylorT4 and Spinning Effective One Body fitted to Numerical Relativity, SEOBNR) are considered in the spin-aligned and precessing cases, in the parameter ranges where the larger spin dominates over the orbital angular momentum. The degeneracy in the parameter space of each waveform is analyzed, then the matches among the waveforms are investigated. Our results show that in the spin-aligned case only the inspiral Spin-dominated and SpinTaylorT4 waveforms agree well with each other. The highest matches of these with SEOBNR are at different parameters as compared to where SEOBNR shows the best match with itself, reflecting SEOBNR being full inspiral-merger-ringdown waveform, with coefficients fitted to numerical relativity, rather than arising from post-Newtonian (PN) calculations. In the precessing case, the matches between the pairs of all waveforms are significantly lower. We identify possible causes of this in (1) the implementation of the angular dynamics carried out at different levels of accuracy for different waveforms; (2) differences in the inclusiveness of the merger process and in the PN coefficients of the inspiral waveforms (Spin-Dominated, SpinTaylorT4) and the full SEOBNR waveform. Full article

(This article belongs to the Special Issue BGL2017: 10th Bolyai-Gauss-Lobachevsky Conference on Non-Euclidean Geometry and Its Applications)

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Open AccessArticle

On Maximal Homogeneous 3-Geometries—A Polyhedron Algorithm for Space Tilings

István Prok

Universe 2018, 4(3), 49; https://doi.org/10.3390/universe4030049 - 06 Mar 2018

Cited by 2 | Viewed by 2602

Abstract

In this paper we introduce a polyhedron algorithm that has been developed for finding space groups. In order to demonstrate the problem and the main steps of the algorithm, we consider some regular plane tilings in our examples, and then we generalize the method for 3-dimensional spaces. Applying the algorithm and its computer implementation we investigate periodic, face-to-face, regular polyhedron tilings in 3-spaces of constant curvature and of the other homogeneous 3-geometries, too. We summarize and visualize the most important results, emphasizing the fixed-point-free space groups which determine 3-dimensional manifolds. Full article

(This article belongs to the Special Issue BGL2017: 10th Bolyai-Gauss-Lobachevsky Conference on Non-Euclidean Geometry and Its Applications)

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Open AccessFeature PaperArticle

Light-Like Shockwaves in Scalar-Tensor Theories

Bence Racskó

and

László Árpád Gergely

Universe 2018, 4(3), 44; https://doi.org/10.3390/universe4030044 - 27 Feb 2018

Cited by 3 | Viewed by 2071

Abstract

Both electromagnetic shock-waves and gravitational waves propagate with the speed of light. If they carry significant energy-momentum, this will change the properties of the space-time they propagate through. This can be described in terms of the junction conditions between space-time regions separated by a singular, null hypersurface. We derived generic junction conditions for Brans-Dicke theory in the Jordan frame, exploring a formalism based on a transverse vector, rather than normal, which can be applied to any type of hypersurfaces. In the particular case of a non-null hypersurface we obtain a generalised Lanczos equation, in which the jump of the extrinsic curvature is sourced by both the distributional energy-momentum tensor and by the jump in the transverse derivative of the scalar. In the case of null hypersurfaces, the distributional source is decomposed into surface density, current and pressure. The latter, however, ought to vanish by virtue of the scalar junction condition. Full article

(This article belongs to the Special Issue BGL2017: 10th Bolyai-Gauss-Lobachevsky Conference on Non-Euclidean Geometry and Its Applications)

Open AccessArticle

Precessing Black Hole Binaries and Their Gravitational Radiation

László Á. Gergely

Zoltán Keresztes

and

Márton Tápai

Universe 2018, 4(2), 40; https://doi.org/10.3390/universe4020040 - 16 Feb 2018

Viewed by 2687

Abstract

The first and second observational runs of Advanced Laser Interferometer Gravitational-wave Observatory (LIGO) have marked the first direct detections of gravitational waves, either from black hole binaries or, in one case, from coalescing neutron stars. These observations opened up the era of gravitational wave astronomy, but also of gravitational wave cosmology, in the form of an independent derivation of the Hubble constant. They were equally important to prove false a plethora of modified gravity theories predicting gravitational wave propagation speed different from that of light. For a continued and improved testing of general relativity, the precise description of compact binary dynamics, not only in the final coalescence phase but also earlier, when precessional effects dominate, are required. We report on the derivation of the full secular dynamics for compact binaries, valid over the precessional time-scale, in the form of an autonomous closed system of differential equations for the set of spin angles and periastron. The system can be applied for mapping the parameter space for the occurrence of the spin flip-flop effect and for more accurately analyzing the spin-flip effect, which could explain the formation of X-shaped radio galaxies. Full article

(This article belongs to the Special Issue BGL2017: 10th Bolyai-Gauss-Lobachevsky Conference on Non-Euclidean Geometry and Its Applications)

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Open AccessArticle

Geometric Aspects and Some Uses of Deformed Models of Thermostatistics

Alexandre Gavrilik

Universe 2018, 4(2), 33; https://doi.org/10.3390/universe4020033 - 11 Feb 2018

Cited by 4 | Viewed by 2348

Abstract

We consider diverse deformed Bose gas models (DBGMs) focusing on distributions and correlations of any order, and also on deformed thermodynamics. For so-called

μ

-deformed Bose gas model (

μ

-DBGM), main thermodynamic aspects are treated: total number of particles, deformed partition function, [...] Read more.

We consider diverse deformed Bose gas models (DBGMs) focusing on distributions and correlations of any order, and also on deformed thermodynamics. For so-called

μ

-deformed Bose gas model (

μ

-DBGM), main thermodynamic aspects are treated: total number of particles, deformed partition function, etc. Using a geometric approach, we confirm the existence of critical behavior—Bose-like condensation; we find the critical temperature

T_{c}^{(μ)}

depending on

μ

so that

T_{c}^{(μ)} > T_{c}^{(Bose)}

for

μ > 0

. This fact and other advantages of

μ

-DBGM relative to the usual Bose gas, e.g., stronger effective inter-particle attraction (controlled by the parameter

μ

), allow us to consider the condensate in

μ

-DBGM as a candidate for modeling dark matter. As another, quite successful application we discuss the usage of the two-parameter (

\tilde{μ}, q

)-deformed BGM for effective description of the peculiar (non-Bose like) behavior of two-pion correlations observed in the STAR experiment at RHIC (Brookhaven). Herein, we point out the transparent role of the two deformation parameters

\tilde{μ}

and q as being responsible for compositeness and (effective account of) interactions of pions, respectively. Full article

(This article belongs to the Special Issue BGL2017: 10th Bolyai-Gauss-Lobachevsky Conference on Non-Euclidean Geometry and Its Applications)

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Open AccessArticle

Centrality Dependent Lévy-Stable Two-Pion Bose-Einstein Correlations in \( {\sqrt{s_{NN}}} \) = 200 GeV Au+Au Collisions at the PHENIX Experiment

Sándor Lökös

Universe 2018, 4(2), 31; https://doi.org/10.3390/universe4020031 - 09 Feb 2018

Cited by 10 | Viewed by 2250

Abstract

Investigation of femtoscopic correlation functions in relativistic heavy ion reactions is an important tool to access the space-time structure of particle production in the strongly interacting Quark Gluon Plasma (sQGP). The shape of the source, and thus the shape of the correlation functions, is often assumed to be Gaussian, but experimental results found evidence for heavy tails in the source distribution of pions. Recent analysis revealed that the statistically correct assumption could be the so-called Lévy distribution. The detailed investigation of correlation functions in various systems may shed light on the location of the critical endpoint on QCD (Quantum Chromodynamics) phase diagram. It could also reveal if there is partially coherent pion production or could indicate the possible in-medium mass modification of the

η^{'}

meson due to the (partial) restoration of the

U_{A} (1)

axial symmetry. These phenomena could depend on the system size and on the collision energy. A detailed centrality-dependent analysis could explore the multiplicity dependencies of the Lévy parameters, and thus the critical and thermodynamical properties of the sQGP, and could give information about the above mentioned processes. In this paper, we present the status of the centrality dependent measurements of two-pion Lévy Bose-Einstein correlation functions

\sqrt{s_{NN}} = 200

GeV Au+Au collisions at PHENIX.
Full article

(This article belongs to the Special Issue BGL2017: 10th Bolyai-Gauss-Lobachevsky Conference on Non-Euclidean Geometry and Its Applications)

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Open AccessArticle

Exclusive Particle Production in pp and pPb Collisions at CMS

Oliver Suranyi

Universe 2018, 4(2), 25; https://doi.org/10.3390/universe4020025 - 05 Feb 2018

Viewed by 2436

Abstract

Exclusive processes provide a useful method to study a broad range of high energy physics fields from gluon density evolutions to searches for new physics. Three measurements from the Compact Muon Solenoid experiment are reviewed. Exclusive

π π

production is studied in proton–proton [...] Read more.

π π

production is studied in proton–proton collisions. Low-mass meson resonances are observed in the invariant mass distribution of pion pairs. The total exclusive

π^{+} π^{-}

cross-section is also measured in the

p_{T} (π) > 0.2

GeV,

| y | < 2

region, yielding

26.5 \pm 0.3 (stat) \pm 5.0 (syst) \pm 1.1 (lumi) μ

b. The photoproduction of

Y (n S)

mesons is observed in ultraperipheral pPb collisions. The differential cross-sections are measured as a function of

| t |

and y. The comparison with previous measurements and theoretical models provides a better understanding of the gluon density evolution at low x values. Evidence for the

γ γ \to W^{+} W^{-}

process is shown with a

3.7 σ

observed significance. According to the results, limits on anomalous quartic gauge couplings can be provided. Full article

(This article belongs to the Special Issue BGL2017: 10th Bolyai-Gauss-Lobachevsky Conference on Non-Euclidean Geometry and Its Applications)

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Open AccessArticle

On the High-Energy Neutrino Emission from Active Galactic Nuclei

and

Universe 2018, 4(2), 24; https://doi.org/10.3390/universe4020024 - 01 Feb 2018

Cited by 3 | Viewed by 2633

Abstract

We review observational aspects of the active galactic nuclei and their jets in connection with the detection of high-energy neutrinos by the Antarctic IceCube Neutrino Observatory. We propose that a reoriented jet generated by the spin-flipping supermassive black hole in a binary merger is likely the source of such high-energy neutrinos. Hence they encode important information on the afterlife of coalescing supermassive black hole binaries. As the gravitational radiation emanating from them will be monitored by the future LISA space mission, high-energy neutrino detections could be considered a contributor to multi-messenger astronomy. Full article

(This article belongs to the Special Issue BGL2017: 10th Bolyai-Gauss-Lobachevsky Conference on Non-Euclidean Geometry and Its Applications)

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Open AccessArticle

Non-Euclidean Geometry, Nontrivial Topology and Quantum Vacuum Effects

Yurii A. Sitenko

and

Volodymyr M. Gorkavenko

Universe 2018, 4(2), 23; https://doi.org/10.3390/universe4020023 - 31 Jan 2018

Cited by 1 | Viewed by 2071

Abstract

Space out of a topological defect of the Abrikosov–Nielsen–Olesen (ANO) vortex type is locally flat but non-Euclidean. If a spinor field is quantized in such a space, then a variety of quantum effects are induced in the vacuum. On the basis of the continuum model for long-wavelength electronic excitations originating in the tight-binding approximation for the nearest-neighbor interaction of atoms in the crystal lattice, we consider quantum ground-state effects in Dirac materials with two-dimensional monolayer structures warped into nanocones by a disclination; the nonzero size of the disclination is taken into account, and a boundary condition at the edge of the disclination is chosen to ensure self-adjointness of the Dirac–Weyl Hamiltonian operator. We show that the quantum ground-state effects are independent of the disclination size, and we find circumstances in which they are independent of parameters of the boundary condition. Full article

(This article belongs to the Special Issue BGL2017: 10th Bolyai-Gauss-Lobachevsky Conference on Non-Euclidean Geometry and Its Applications)

Open AccessFeature PaperArticle

Scaling Properties of the Mean Multiplicity and Pseudorapidity Density in e⁻+e⁺, e^±+p, p( p ¯ )+p, p+A and A+A(B) Collisions

Nuggehalli N. Ajitanand

John Alexander

and

Robert Pak

Universe 2018, 4(1), 22; https://doi.org/10.3390/universe4010022 - 22 Jan 2018

Cited by 15 | Viewed by 2102

Abstract

The charged-particle pseudorapidity density (

d N_{ch} / d η

) for p(

\bar{p}

)+p, p+A and A+A(B) collisions and the mean multiplicity

⟨ N_{ch} ⟩

for e

^{-}

^{+}

e^{\pm} + p

, and p( [...] Read more.

The charged-particle pseudorapidity density (

d N_{ch} / d η

) for p(

\bar{p}

)+p, p+A and A+A(B) collisions and the mean multiplicity

〈 N_{ch} 〉

for e

^{-}

^{+}

e^{\pm} + p

, and p(

\bar{p}

)+p collisions are studied for a wide range of beam energies (

\sqrt{s}

). Characteristic scaling patterns are observed for both

d N_{ch} / d η

and

〈 N_{ch} 〉

, consistent with a thermal particle production mechanism for the bulk of the soft particles created in all of these systems. The scaling patterns found also validate an essential role for quark participants in these collisions. The measured values for

d N_{ch} / d η

and

〈 N_{ch} 〉

are observed to factorize into contributions that depend on

log (\sqrt{s})

and the number of nucleon or quark participant pairs

N_{pp}

. The quantification of these contributions gives expressions that serve to systematize

d N_{ch} / d η

and

〈 N_{ch} 〉

measurements spanning nearly 4 orders of magnitude in

\sqrt{s}

and to predict their values as a function of

\sqrt{s}

and

N_{pp}

. Full article

(This article belongs to the Special Issue BGL2017: 10th Bolyai-Gauss-Lobachevsky Conference on Non-Euclidean Geometry and Its Applications)

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Open AccessArticle

Pure-Connection Gravity and Anisotropic Singularities

Kirill Krasnov

and

Yuri Shtanov

Universe 2018, 4(1), 12; https://doi.org/10.3390/universe4010012 - 04 Jan 2018

Cited by 2 | Viewed by 2083

Abstract

In four space-time dimensions, there exists a special infinite-parameter family of chiral modified gravity theories. They are most properly described by a connection field, with space-time metric being a secondary and derived concept. All these theories have the same number of degrees of freedom as general relativity, which is the only parity-invariant member of this family. Modifications of general relativity can be arranged so as to become important in regions with large curvature. In this paper, we review how a certain simple modification of this sort can resolve the Schwarzschild black-hole and Kasner anisotropic singularities of general relativity. In the corresponding solutions, the fundamental connection field is regular in space-time. Full article

(This article belongs to the Special Issue BGL2017: 10th Bolyai-Gauss-Lobachevsky Conference on Non-Euclidean Geometry and Its Applications)

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Open AccessArticle

Lévy Analysis of HBT Correlation Functions in s N N = 62 GeV and 39 GeV Au + Au Collisions at PHENIX

Dániel Kincses

Universe 2018, 4(1), 11; https://doi.org/10.3390/universe4010011 - 04 Jan 2018

Cited by 8 | Viewed by 2184

Abstract

The phase diagram of strongly interacting matter can be explored by analyzing data of heavy-ion collisions at different center of mass collision energies. For investigating the space-time structure of the hadron emission source, Bose-Einstein or HBT correlation measurements are among the best tools. [...] Read more.

\sqrt{s_{N N}} =

39 GeV and 62 GeV Au + Au collisions. Full article

(This article belongs to the Special Issue BGL2017: 10th Bolyai-Gauss-Lobachevsky Conference on Non-Euclidean Geometry and Its Applications)

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Open AccessArticle

Entropic Distance for Nonlinear Master Equation

Tamás Sándor Biró

András Telcs

and

Zoltán Néda

Universe 2018, 4(1), 10; https://doi.org/10.3390/universe4010010 - 04 Jan 2018

Cited by 3 | Viewed by 2110

Abstract

More and more works deal with statistical systems far from equilibrium, dominated by unidirectional stochastic processes, augmented by rare resets. We analyze the construction of the entropic distance measure appropriate for such dynamics. We demonstrate that a power-like nonlinearity in the state probability in the master equation naturally leads to the Tsallis (Havrda–Charvát, Aczél–Daróczy) q-entropy formula in the context of seeking for the maximal entropy state at stationarity. A few possible applications of a certain simple and linear master equation to phenomena studied in statistical physics are listed at the end. Full article

(This article belongs to the Special Issue BGL2017: 10th Bolyai-Gauss-Lobachevsky Conference on Non-Euclidean Geometry and Its Applications)

Open AccessArticle

Hamiltonian Dynamics of Doubly-Foliable Space-Times

Cecília Gergely

Zoltán Keresztes

and

László Árpád Gergely

Universe 2018, 4(1), 9; https://doi.org/10.3390/universe4010009 - 03 Jan 2018

Cited by 1 | Viewed by 2153

Abstract

The 2 + 1 + 1 decomposition of space-time is useful in monitoring the temporal evolution of gravitational perturbations/waves in space-times with a spatial direction singled-out by symmetries. Such an approach based on a perpendicular double foliation has been employed in the framework of dark matter and dark energy-motivated scalar-tensor gravitational theories for the discussion of the odd sector perturbations of spherically-symmetric gravity. For the even sector, however, the perpendicularity has to be suppressed in order to allow for suitable gauge freedom, recovering the 10th metric variable. The 2 + 1 + 1 decomposition of the Einstein–Hilbert action leads to the identification of the canonical pairs, the Hamiltonian and momentum constraints. Hamiltonian dynamics is then derived via Poisson brackets. Full article

(This article belongs to the Special Issue BGL2017: 10th Bolyai-Gauss-Lobachevsky Conference on Non-Euclidean Geometry and Its Applications)

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Open AccessArticle

Parallels of Belated Recognition: Bolyai János and Károlyházy Frigyes

György Kádár

Universe 2018, 4(1), 8; https://doi.org/10.3390/universe4010008 - 03 Jan 2018

Viewed by 2342

Abstract

There was an obvious parallelism between the lives of the two Hungarian men of science: János Bolyai a genial geometer and Frigyes Károlyházy a missionary of education in the field of modern physics. Both of them selected and solved a complex problem that was too difficult for the majority of scientists of their times. Their work was criticized authoritatively by high rank scientists of their discipline, which led to their withdrawal from science. The belated recognition of the Non-Euclidean geometry and the gravity inspired quantum-mechanical state reduction put these excellent achievements to their deserved right place. Full article

(This article belongs to the Special Issue BGL2017: 10th Bolyai-Gauss-Lobachevsky Conference on Non-Euclidean Geometry and Its Applications)

Open AccessArticle

Universal Hyperbolic Geometry, Sydpoints and Finite Fields: A Projective and Algebraic Alternative

Norman J. Wildberger

Universe 2018, 4(1), 3; https://doi.org/10.3390/universe4010003 - 01 Jan 2018

Viewed by 4260

Abstract

Universal hyperbolic geometry gives a purely algebraic approach to the subject that connects naturally with Einstein’s special theory of relativity. In this paper, we give an overview of some aspects of this theory relating to triangle geometry and in particular the remarkable new analogues of midpoints called sydpoints. We also discuss how the generality allows us to consider hyperbolic geometry over general fields, in particular over finite fields. Full article

(This article belongs to the Special Issue BGL2017: 10th Bolyai-Gauss-Lobachevsky Conference on Non-Euclidean Geometry and Its Applications)

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Open AccessArticle

Lévy Femtoscopy with PHENIX at RHIC

Máté Csanád

Universe 2017, 3(4), 85; https://doi.org/10.3390/universe3040085 - 18 Dec 2017

Cited by 7 | Viewed by 2429

Abstract

In this paper we present the measurement of charged pion two-particle femtoscopic correlation functions in

\sqrt{s_{N N}} = 200

GeV Au + Au collisions in 31 average transverse mass bins, separately for positive and negative pion pairs. Lévy-shaped source distributions yield a [...] Read more.

In this paper we present the measurement of charged pion two-particle femtoscopic correlation functions in

\sqrt{s_{N N}} = 200

GeV Au + Au collisions in 31 average transverse mass bins, separately for positive and negative pion pairs. Lévy-shaped source distributions yield a statistically acceptable description of the measured correlation functions, with three physical parameters: correlation strength parameter

λ

, Lévy index

α

and Lévy scale parameter R. The transverse mass dependence of these Lévy parameters is then investigated. Their physical interpretation is also discussed, and the appearance of a new scaling variable is observed. Full article

(This article belongs to the Special Issue BGL2017: 10th Bolyai-Gauss-Lobachevsky Conference on Non-Euclidean Geometry and Its Applications)

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Open AccessArticle

Perturbative Accelerating Solutions of Relativistic Hydrodynamics

Bálint Kurgyis

and

Máté Csanád

Universe 2017, 3(4), 84; https://doi.org/10.3390/universe3040084 - 14 Dec 2017

Cited by 4 | Viewed by 2430

Abstract

In ultra-relativistic collisions of heavy ions, the strongly interacting Quark Gluon Plasma (sQGP) is created. The fluid nature of the sQGP was one of the important discoveries of high energy heavy ion physics in the last decades. Henceforth the explosion of this matter may be described by hydrodynamical models. Besides numerical simulations, it is important to study the analytic solutions of the equations of hydrodynamics, as these enable us to understand the connection of the final and initial states better. In this paper we present a perturbative, accelerating solution of relativistic hydrodynamics, on top of a known class of solutions describing Hubble-expansion. We describe the properties of this class of perturbative solutions, and investigate a few selected solutions in detail. Full article

(This article belongs to the Special Issue BGL2017: 10th Bolyai-Gauss-Lobachevsky Conference on Non-Euclidean Geometry and Its Applications)

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Open AccessArticle

On Maximal Homogeneous 3-Geometries and Their Visualization

Emil Molnár

István Prok

and

Jeno Szirmai

Universe 2017, 3(4), 83; https://doi.org/10.3390/universe3040083 - 04 Dec 2017

Cited by 2 | Viewed by 3026

Abstract

The motivation for this talk and paper is related to the classification of the homogeneous simply connected maximal 3-geometries (the so-called Thurston geometries:

E^{3}

S^{3}

H^{3}

S^{2} \times R

H^{2} \times R

, [...] Read more.

The motivation for this talk and paper is related to the classification of the homogeneous simply connected maximal 3-geometries (the so-called Thurston geometries:

E^{3}

S^{3}

H^{3}

S^{2} \times R

H^{2} \times R

\tilde{S L_{2} R}

Nil

, and

Sol

) and their applications in crystallography. The first author found in (Molnár 1997) (see also the more popular (Molnár et al. 2010; 2015) with co-author colleagues, together with more details) a unified projective interpretation for them in the sense of Felix Klein’s Erlangen Program: namely, each S of the above space geometries and its isometry group

Isom (S)

can be considered as a subspace of the projective 3-sphere:

S \subset P S^{3}

, where a special maximal group

G = Isom (S) \subseteq Coll (P S^{3})

of collineations acts, leaving the above subspace S invariant. Vice-versa, we can start with the projective geometry, namely with the classification of

Coll (P S^{3})

through linear transforms of dual pairs of real 4-vector spaces

(V^{4}, V_{4}, R, \sim)

P S^{3}

(up to positive real multiplicative equivalence ∼) via Jordan normal forms. Then, we look for projective groups with 3 parameters, and with appropriate properties for convenient geometries described above and in this paper. Full article

(This article belongs to the Special Issue BGL2017: 10th Bolyai-Gauss-Lobachevsky Conference on Non-Euclidean Geometry and Its Applications)

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Open AccessArticle

Enhancement of Elliptic Flow of π⁻ under Intense Magnetic Field in √ ^sNN = 200 GeV Au+Au Collisions: A (2 + 1)-Dimensional Reduced-MHD Model Study

Victor Roy

Universe 2017, 3(4), 82; https://doi.org/10.3390/universe3040082 - 30 Nov 2017

Cited by 2 | Viewed by 1891

Abstract

We investigate the effect of intense magnetic fields on the

(2 + 1)

-dimensional reduced- magnetohydrodynamical (MHD) expansion of hot and dense quark–gluon plasma (QGP) produced in

\sqrt{s_{NN}}

= 200 GeV Au+Au collisions. For the sake of simplicity, we consider [...] Read more.

We investigate the effect of intense magnetic fields on the

(2 + 1)

-dimensional reduced- magnetohydrodynamical (MHD) expansion of hot and dense quark–gluon plasma (QGP) produced in

\sqrt{s_{NN}}

= 200 GeV Au+Au collisions. For the sake of simplicity, we consider the case in which the magnetic field points in the direction perpendicular to the reaction plane. We also consider this field to be external, with energy density parametrized as a two-dimensional Gaussian. The width of the Gaussian along the directions orthogonal to the beam axis varies with the centrality of the collision. The dependence of the magnetic field on proper time (

τ

) is parametrized for the case of zero and finite electrical conductivity of the QGP. We solve the equations of motion of ideal hydrodynamics for such an external magnetic field. For collisions with a non-zero impact parameter we observe a considerable increase in the elliptic-flow coefficient

v_{2}

π^{-}

in the presence of an external magnetic field, and the increment in

v_{2}

is found to depend on the evolution and the initial magnitude of the magnetic field. Full article

(This article belongs to the Special Issue BGL2017: 10th Bolyai-Gauss-Lobachevsky Conference on Non-Euclidean Geometry and Its Applications)

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Open AccessArticle

Effective Interactions and Prospects for Resolution of the Fundamental Cosmological Problems in Quantum Gravity

Boris A. Arbuzov

Universe 2017, 3(4), 80; https://doi.org/10.3390/universe3040080 - 15 Nov 2017

Viewed by 3274

Abstract

Wouldbe consequences of the existence of effective interactions in quantum gravitation theory are considered. In the framework of the approach, the example of a running gravitational coupling is presented, corresponding to an adequate description of effects, which nowadays are usually prescribed to dark [...] Read more.

(This article belongs to the Special Issue BGL2017: 10th Bolyai-Gauss-Lobachevsky Conference on Non-Euclidean Geometry and Its Applications)

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Open AccessFeature PaperArticle

Femtoscopy with Identified Hadrons in pp, pPb, and PbPb Collisions in CMS

Ferenc Siklér

Universe 2017, 3(4), 76; https://doi.org/10.3390/universe3040076 - 08 Nov 2017

Cited by 3 | Viewed by 2555

Abstract

Short-range correlations of identified charged hadrons in pp (

\sqrt{s} =

0.9, 2.76, and 7 TeV), pPb (

\sqrt{s_{_{NN}}} =

5.02 TeV), and peripheral PbPb collisions (

\sqrt{s_{_{NN}}} =

2.76 TeV) are studied with the CMS detector at the LHC. Charged [...] Read more.

Short-range correlations of identified charged hadrons in pp (

\sqrt{s} =

0.9, 2.76, and 7 TeV), pPb (

\sqrt{s_{_{NN}}} =

5.02 TeV), and peripheral PbPb collisions (

\sqrt{s_{_{NN}}} =

2.76 TeV) are studied with the CMS detector at the LHC. Charged pions, kaons, and protons at low momentum and in laboratory pseudorapidity

| η | < 1

are identified via their energy loss in the silicon tracker. The two-particle correlation functions show effects of quantum statistics, Coulomb interaction, and also indicate the role of multi-body resonance decays and mini-jets. The characteristics of the one-, two-, and three-dimensional correlation functions are studied as a function of transverse pair momentum,

k_{T}

, and the charged-particle multiplicity of the event. The extracted radii are in the range 1–5 fm, reaching highest values for very high multiplicity pPb, also for similar multiplicity PbPb collisions, and decrease with increasing

k_{T}

. The dependence of radii on multiplicity and

k_{T}

largely factorizes and appears to be insensitive to the type of the colliding system and center-of-mass energy. Full article

(This article belongs to the Special Issue BGL2017: 10th Bolyai-Gauss-Lobachevsky Conference on Non-Euclidean Geometry and Its Applications)

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Jump to: Research

Open AccessConference Report

Geometry of Bigravity

Vladimir Soloviev

Universe 2018, 4(2), 19; https://doi.org/10.3390/universe4020019 - 31 Jan 2018

Cited by 1 | Viewed by 1819

Abstract

The non-Euclidean geometry created by Bolyai, Lobachevsky and Gauss has led to a new physical theory—general relativity. In due turn, a correct mathematical treatment of the cosmological problem in general relativity has led Friedmann to a discovery of dynamical equations for the universe. And now, after almost a century of theoretical and experimental research, cosmology has a status of the most rapidly developing fundamental science. New challenges here are problems of dark energy and dark matter. As a result, a lot of modifications of general relativity appear recently. The bigravity is one of them, constructed with a couple of interacting space–time metrics accompanied by some coupling to matter. We discuss here this approach and different kinds of the coupling. Full article

(This article belongs to the Special Issue BGL2017: 10th Bolyai-Gauss-Lobachevsky Conference on Non-Euclidean Geometry and Its Applications)

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