Markov random field models of multicasting in tree networks

2002 ◽  
Vol 34 (01) ◽  
pp. 58-84 ◽  
Author(s):  
Kavita Ramanan ◽  
Anirvan Sengupta ◽  
Ilze Ziedins ◽  
Partha Mitra
Keyword(s):  
Phase Transition ◽  
Fixed Point ◽  
Phase Transitions ◽  
Large Network ◽  
Regular Tree ◽  
The Core ◽  
Markov Random ◽  
Blocking Probabilities ◽  
Unit Capacity ◽  
Single Link

In this paper, we analyse a model of a regular tree loss network that supports two types of calls: unicast calls that require unit capacity on a single link, and multicast calls that require unit capacity on every link emanating from a node. We study the behaviour of the distribution of calls in the core of a large network that has uniform unicast and multicast arrival rates. At sufficiently high multicast call arrival rates the network exhibits a ‘phase transition’, leading to unfairness due to spatial variation in the multicast blocking probabilities. We study the dependence of the phase transition on unicast arrival rates, the coordination number of the network, and the parity of the capacity of edges in the network. Numerical results suggest that the nature of phase transitions is qualitatively different when there are odd and even capacities on the links. These phenomena are seen to persist even with the introduction of nonuniform arrival rates and multihop multicast calls into the network. Finally, we also show the inadequacy of approximations such as the Erlang fixed-point approximations when multicasting is present.

Markov random field models of multicasting in tree networks

2002 ◽  
Vol 34 (1) ◽  
pp. 58-84 ◽  
Author(s):  
Kavita Ramanan ◽  
Anirvan Sengupta ◽  
Ilze Ziedins ◽  
Partha Mitra
Keyword(s):  
Phase Transition ◽  
Fixed Point ◽  
Phase Transitions ◽  
Large Network ◽  
Regular Tree ◽  
The Core ◽  
Markov Random ◽  
Blocking Probabilities ◽  
Unit Capacity ◽  
Single Link

In this paper, we analyse a model of a regular tree loss network that supports two types of calls: unicast calls that require unit capacity on a single link, and multicast calls that require unit capacity on every link emanating from a node. We study the behaviour of the distribution of calls in the core of a large network that has uniform unicast and multicast arrival rates. At sufficiently high multicast call arrival rates the network exhibits a ‘phase transition’, leading to unfairness due to spatial variation in the multicast blocking probabilities. We study the dependence of the phase transition on unicast arrival rates, the coordination number of the network, and the parity of the capacity of edges in the network. Numerical results suggest that the nature of phase transitions is qualitatively different when there are odd and even capacities on the links. These phenomena are seen to persist even with the introduction of nonuniform arrival rates and multihop multicast calls into the network. Finally, we also show the inadequacy of approximations such as the Erlang fixed-point approximations when multicasting is present.

scholarly journals Phase transitions in neutron stars

2018 ◽  
Vol 27 (11) ◽  
pp. 1830008 ◽  
Author(s):  
V. Dexheimer ◽  
L. T. T. Soethe ◽  
J. Roark ◽  
R. O. Gomes ◽  
S. O. Kepler ◽  
...  
Keyword(s):  
Phase Transition ◽  
Phase Transitions ◽  
Equation Of State ◽  
Neutron Stars ◽  
Order Phase Transition ◽  
Dense Matter ◽  
First Order ◽  
The Core ◽  
First Order Phase Transition ◽  
First Order Phase

In this paper, we review the most common descriptions for the first-order phase transition to deconfined quark matter in the core of neutron stars. We also present a new description of these phase transitions in the core of proto-neutron stars, in which more constraints are enforced so as to include trapped neutrinos. Finally, we calculate the emission of gravitational waves associated with deconfinement phase transitions, discuss the possibility of their detection, and how this would provide information about the equation of state of dense matter.

scholarly journals Supersymmetry breaking deformations and phase transitions in five dimensions

2021 ◽  
Vol 2021 (10) ◽  
Author(s):  
Matteo Bertolini ◽  
Francesco Mignosa
Keyword(s):  
Phase Transition ◽  
Fixed Point ◽  
Phase Transitions ◽  
Supersymmetry Breaking ◽  
Gauge Coupling ◽  
Global Symmetry ◽  
Five Dimensions ◽  
Yang Mills ◽  
New Phase ◽  
Mass Deformation

Abstract We analyze a recently proposed supersymmetry breaking mass deformation of the E1 superconformal fixed point in five dimensions which, at weak gauge coupling, leads to pure SU(2) Yang-Mills and which was conjectured to lead to an interacting CFT at strong coupling. We provide an explicit geometric construction of the deformation using brane-web techniques and show that for large enough gauge coupling a global symmetry is spontaneously broken and the theory enters a new phase which, at infinite coupling, displays an instability. The Yang-Mills and the symmetry broken phases are separated by a phase transition. Depending on the structure of the potential, this can be first or second order.

scholarly journals Electric properties of olive oil under pressure

2021 ◽  
Author(s):  
L. T. Pawlicki ◽  
R. M. Siegoczyński ◽  
S. Ptasznik ◽  
K. Marszałek
Keyword(s):  
Molecular Structure ◽  
Phase Transition ◽  
Phase Diagram ◽  
Phase Transitions ◽  
Olive Oil ◽  
Material Parameters ◽  
First Order ◽  
Long Time ◽  
Capacitive Reactance ◽  
First Order Phase

AbstractThe main purpose of the experiment was a thermodynamic research with use of the electric methods chosen. The substance examined was olive oil. The paper presents the resistance, capacitive reactance, relative permittivity and resistivity of olive. Compression was applied with two mean velocities up to 450 MPa. The results were shown as functions of pressure and time and depicted on the impedance phase diagram. The three first order phase transitions have been detected. All the changes in material parameters were observed during phase transitions. The material parameters measured turned out to be the much more sensitive long-time phase transition factors than temperature. The values of material parameters and their dependence on pressure and time were compared with the molecular structure, arrangement of molecules and interactions between them. Knowledge about olive oil parameters change with pressure and its phase transitions is very important for olive oil production and conservation.

Room-temperature NaI/H2O compression icing: solute–solute interactions

2017 ◽  
Vol 19 (39) ◽  
pp. 26645-26650 ◽  
Author(s):  
Qingxin Zeng ◽  
Chuang Yao ◽  
Kai Wang ◽  
Chang Q. Sun ◽  
Bo Zou
Keyword(s):  
Phase Transition ◽  
Phase Transitions ◽  
Bond Energy ◽  
Room Temperature ◽  
Solute Concentration ◽  
Solute Interaction ◽  
Solute Interactions

H–O bond energy governs the PCx for Na/H2O liquid–VI–VII phase transition. Solute concentration affects the path of phase transitions differently with the solute type. Solute–solute interaction lessens the PC2 sensitivity to compression. The PC1 goes along the liquid–VI boundary till the triple phase joint.

scholarly journals The origin of the lattice thermal conductivity enhancement at the ferroelectric phase transition in GeTe

2021 ◽  
Vol 7 (1) ◽  
Author(s):  
Đorđe Dangić ◽  
Olle Hellman ◽  
Stephen Fahy ◽  
Ivana Savić
Keyword(s):  
Phase Transition ◽  
Thermal Conductivity ◽  
Phase Transitions ◽  
Thermoelectric Materials ◽  
Ferroelectric Phase Transition ◽  
Lattice Thermal Conductivity ◽  
Ferroelectric Phase ◽  
Structural Phase ◽  
High Symmetry ◽  
Structural Phase Transitions

AbstractThe proximity to structural phase transitions in IV-VI thermoelectric materials is one of the main reasons for their large phonon anharmonicity and intrinsically low lattice thermal conductivity κ. However, the κ of GeTe increases at the ferroelectric phase transition near 700 K. Using first-principles calculations with the temperature dependent effective potential method, we show that this rise in κ is the consequence of negative thermal expansion in the rhombohedral phase and increase in the phonon lifetimes in the high-symmetry phase. Strong anharmonicity near the phase transition induces non-Lorentzian shapes of the phonon power spectra. To account for these effects, we implement a method of calculating κ based on the Green-Kubo approach and find that the Boltzmann transport equation underestimates κ near the phase transition. Our findings elucidate the influence of structural phase transitions on κ and provide guidance for design of better thermoelectric materials.

scholarly journals Thermal, ferroelastic, and structural properties near phase transitions of organic–inorganic perovskite type [NH3(CH2)3NH3]CdBr4 crystals

RSC Advances ◽  
2021 ◽  
Vol 11 (29) ◽  
pp. 17622-17629
Author(s):  
Ae Ran Lim
Keyword(s):  
Phase Transition ◽  
Phase Transitions ◽  
Thermal Behavior ◽  
Structural Properties ◽  
Structural Dynamics ◽  
Transition Temperatures ◽  
Inorganic Perovskite ◽  
Phase Transition Temperatures ◽  
Perovskite Type

We studied the thermal behavior and structural dynamics of [NH3(CH2)3NH3]CdBr4 near phase transition temperatures.

scholarly journals Phase transition of the 2-Choices dynamics on core–periphery networks

2021 ◽  
Author(s):  
Emilio Cruciani ◽  
Emanuele Natale ◽  
André Nusser ◽  
Giacomo Scornavacca
Keyword(s):  
Phase Transition ◽  
Voting Behavior ◽  
Structural Parameters ◽  
Connected Subset ◽  
Transition Phenomenon ◽  
The Core ◽  
Analytical Results ◽  
Heterogeneous Behavior

AbstractThe 2-Choices dynamics is a process that models voting behavior on networks and works as follows: Each agent initially holds either opinion blue or red; then, in each round, each agent looks at two random neighbors and, if the two have the same opinion, the agent adopts it. We study its behavior on a class of networks with core–periphery structure. Assume that a densely-connected subset of agents, the core, holds a different opinion from the rest of the network, the periphery. We prove that, depending on the strength of the cut between core and periphery, a phase-transition phenomenon occurs: Either the core’s opinion rapidly spreads across the network, or a metastability phase takes place in which both opinions coexist for superpolynomial time. The interest of our result, which we also validate with extensive experiments on real networks, is twofold. First, it sheds light on the influence of the core on the rest of the network as a function of its connectivity toward the latter. Second, it is one of the first analytical results which shows a heterogeneous behavior of a simple dynamics as a function of structural parameters of the network.

scholarly journals Symmetry breaking at high temperatures in large N gauge theories

2021 ◽  
Vol 2021 (8) ◽  
Author(s):  
Soumyadeep Chaudhuri ◽  
Eliezer Rabinovici
Keyword(s):  
Fixed Point ◽  
Phase Transitions ◽  
Symmetry Breaking ◽  
High Temperatures ◽  
Gauge Theories ◽  
Scalar Fields ◽  
Temperature Limit ◽  
Spontaneous Breaking ◽  
Critical Temperatures ◽  
Weakly Coupled

Abstract Considering marginally relevant and relevant deformations of the weakly coupled (3 + 1)-dimensional large N conformal gauge theories introduced in [1], we study the patterns of phase transitions in these systems that lead to a symmetry-broken phase in the high temperature limit. These deformations involve only the scalar fields in the models. The marginally relevant deformations are obtained by varying certain double trace quartic couplings between the scalar fields. The relevant deformations, on the other hand, are obtained by adding masses to the scalar fields while keeping all the couplings frozen at their fixed point values. At the N → ∞ limit, the RG flows triggered by these deformations approach the aforementioned weakly coupled CFTs in the UV regime. These UV fixed points lie on a conformal manifold with the shape of a circle in the space of couplings. As shown in [1], in certain parameter regimes a subset of points on this manifold exhibits thermal order characterized by the spontaneous breaking of a global ℤ2 or U(1) symmetry and Higgsing of a subset of gauge bosons at all nonzero temperatures. We show that the RG flows triggered by the marginally relevant deformations lead to a weakly coupled IR fixed point which lacks the thermal order. Thus, the systems defined by these RG flows undergo a transition from a disordered phase at low temperatures to an ordered phase at high temperatures. This provides examples of both inverse symmetry breaking and symmetry nonrestoration. For the relevant deformations, we demonstrate that a variety of phase transitions are possible depending on the signs and magnitudes of the squares of the masses added to the scalar fields. Using thermal perturbation theory, we derive the approximate values of the critical temperatures for all these phase transitions. All the results are obtained at the N → ∞ limit. Most of them are found in a reliable weak coupling regime and for others we present qualitative arguments.

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