scholarly journals Stochastic rumors on random trees

2021 ◽  
Vol 2021 (12) ◽  
pp. 123403
Author(s):  
Valdivino V Junior ◽  
Pablo M Rodriguez ◽  
Adalto Speroto
Keyword(s):  
Phase Transition ◽  
Critical Parameter ◽  
Nearest Neighbor ◽  
Critical Value ◽  
Random Trees ◽  
Discrete Distributions ◽  
Positive Probability ◽  
The Mean

Abstract The Maki–Thompson rumor model is defined by assuming that a population represented by a graph is subdivided into three classes of individuals; namely, ignorants, spreaders and stiflers. A spreader tells the rumor to any of its nearest ignorant neighbors at rate one. At the same rate, a spreader becomes a stifler after a contact with other nearest neighbor spreaders, or stiflers. In this work we study the model on random trees. As usual we define a critical parameter of the model as the critical value around which the rumor either becomes extinct almost-surely or survives with positive probability. We analyze the existence of phase-transition regarding the survival of the rumor, and we obtain estimates for the mean range of the rumor. The applicability of our results is illustrated with examples on random trees generated from some well-known discrete distributions.

scholarly journals AN IMPROVED LOWER BOUND FOR THE CRITICAL PARAMETER OF STAVSKAYA’S PROCESS

2020 ◽  
Vol 102 (3) ◽  
pp. 517-524
Author(s):  
ALEX D. RAMOS ◽  
CALITÉIA S. SOUSA ◽  
PABLO M. RODRIGUEZ ◽  
PAULA CADAVID
Keyword(s):  
Phase Transition ◽  
Lower Bound ◽  
Open Problem ◽  
Critical Parameter ◽  
Critical Value ◽  
The State ◽  
Multicomponent Systems ◽  
Dimensional Lattice ◽  
One Dimensional ◽  
Probabilistic Cellular Automaton

We consider Stavskaya’s process, which is a two-state probabilistic cellular automaton defined on a one-dimensional lattice. The state of any vertex depends only on itself and on the state of its right-adjacent neighbour. This process was one of the first multicomponent systems with local interaction for which the existence of a kind of phase transition has been rigorously proved. However, the exact localisation of its critical value remains as an open problem. We provide a new lower bound for the critical value.

The flattening phase transition in systems of trapped ions

2009 ◽  
Vol 87 (10) ◽  
pp. 1425-1435 ◽  
Author(s):  
Taunia L. L. Closson ◽  
Marc R. Roussel
Keyword(s):  
Phase Transition ◽  
Critical Exponent ◽  
Order Parameter ◽  
Ion Trap ◽  
Anisotropy Parameter ◽  
Critical Value ◽  
Trapped Ions ◽  
Dimensional Structure ◽  
Flattening Process ◽  
Second Order Phase Transition

When the anisotropy of a harmonic ion trap is increased, the ions eventually collapse into a two-dimensional structure consisting of concentric shells of ions. This collapse generally behaves like a second-order phase transition. A graph of the critical value of the anisotropy parameter vs. the number of ions displays substructure closely related to the inner-shell configurations of the clusters. The critical exponent for the order parameter of this phase transition (maximum extent in the z direction) was found computationally to have the value β = 1/2. A second critical exponent related to displacements perpendicular to the z axis was found to have the value δ = 1. Using these estimates of the critical exponents, we derive an equation that relates the amplitudes of the displacements of the ions parallel to the x–y plane to the amplitudes along the z axis during the flattening process.

Laser-Induced Pretransitional Ordering And Nonlinear Optical Properties Of Rigid-Rod Polymer Suspensions

1993 ◽  
Vol 328 ◽  
Author(s):  
Boris E. Vugmeister ◽  
Michelle S. Malcuit ◽  
John C. Kralik ◽  
Colleen Stevens
Keyword(s):  
Phase Transition ◽  
Colloidal Particles ◽  
Volume Fraction ◽  
Orientational Order ◽  
Critical Value ◽  
Orientational Relaxation ◽  
First Order ◽  
First Order Phase Transition ◽  
Rigid Rod ◽  
First Order Phase

ABSTRACTWe investigate the pretransitional behavior in laser-induced alignment of rigid rod-like polytetraflouroethylene (PTFE) suspensions. Using a laser-induced birefringence experiment, we measure both the orientational order parameter and the orientational relaxation time. We find that both increase as the volume fraction of colloidal particles approaches the critical value for the isotropic-nematic phase transition. Experimental results are compared with theory which takes into account the possibility of a first-order phase transition induced by a laser electric field.

Analysis of the Real Area of Contact Between a Polymeric Magnetic Medium and a Rigid Surface

1984 ◽  
Vol 106 (1) ◽  
pp. 26-34 ◽  
Author(s):  
Bharat Bhushan
Keyword(s):  
Complex Modulus ◽  
Critical Value ◽  
Computer Applications ◽  
Hard Material ◽  
Rigid Surface ◽  
Magnetic Medium ◽  
The Real ◽  
Real Area Of Contact ◽  
The Mean ◽  
Real Area

The statistical analysis of the real area of contact proposed by Greenwood and Williamson is revisited. General and simplified equations for the mean asperity real area of contact, number of contacts, total real area of contact, and mean real pressure as a function of apparent pressure for the case of elastic junctions are presented. The critical value of the mean asperity pressure at which plastic flow starts when a polymer contacts a hard material is derived. Based on this, conditions of elastic and plastic junctions for polymers are defined by a “polymer” plasticity index, Ψp which depends on the complex modulus, Poisson’s ratio, yield strength, and surface topography. Calculations show that most dynamic contacts that occur in a computer-magnetic tape are elastic, and the predictions are supported by experimental evidence. Tape wear in computer applications is small and decreases Ψp by less than 10 percent. The theory presented here can also be applied to rigid and floppy disks.

scholarly journals Thermodynamic and Elastic Properties of Interstitial Alloy FeC with BCC Structure at Zero Pressure

2018 ◽  
Vol 2018 ◽  
pp. 1-8 ◽  
Author(s):  
Bui Duc Tinh ◽  
Nguyen Quang Hoc ◽  
Dinh Quang Vinh ◽  
Tran Dinh Cuong ◽  
Nguyen Duc Hien
Keyword(s):  
Nearest Neighbor ◽  
Young Modulus ◽  
Thermodynamic Quantities ◽  
Atom Concentration ◽  
Main Metal ◽  
Special Cases ◽  
Analytic Expressions ◽  
Rigidity Modulus ◽  
Bcc Structure ◽  
The Mean

The analytic expressions for the thermodynamic and elastic quantities such as the mean nearest neighbor distance, the free energy, the isothermal compressibility, the thermal expansion coefficient, the heat capacities at constant volume and at constant pressure, the Young modulus, the bulk modulus, the rigidity modulus, and the elastic constants of binary interstitial alloy with body-centered cubic (BCC) structure, and the small concentration of interstitial atoms (below 5%) are derived by the statistical moment method. The theoretical results are applied to interstitial alloy FeC in the interval of temperature from 100 to 1000 K and in the interval of interstitial atom concentration from 0 to 5%. In special cases, we obtain the thermodynamic quantities of main metal Fe with BCC structure. Our calculated results for some thermodynamic and elastic quantities of main metal Fe and alloy FeC are compared with experiments.

STUDY OF THERMODYNAMIC PROPERTIES OF ZINC-BLENDE-TYPE SEMICONDUCTORS: TEMPERATURE AND PRESSURE DEPENDENCES

2011 ◽  
Vol 25 (12n13) ◽  
pp. 1041-1051 ◽  
Author(s):  
HO KHAC HIEU ◽  
VU VAN HUNG
Keyword(s):  
Nearest Neighbor ◽  
Thermodynamic Quantities ◽  
Atomic Displacements ◽  
Zinc Blende ◽  
The Mean ◽  
Temperature And Pressure ◽  
Analytical Expressions ◽  
Theoretical Results ◽  
Nearest Neighbor Distances ◽  
Statistical Moment Method

Using the statistical moment method (SMM), the temperature and pressure dependences of thermodynamic quantities of zinc-blende-type semiconductors have been investigated. The analytical expressions of the nearest-neighbor distances, the change of volumes and the mean-square atomic displacements (MSDs) have been derived. Numerical calculations have been performed for a series of zinc-blende-type semiconductors: GaAs , GaP , GaSb , InAs , InP and InSb . The agreement between our calculations and both earlier other theoretical results and experimental data is a support for our new theory in investigating the temperature and pressure dependences of thermodynamic quantities of semiconductors.

Nonequilibrium Phenomena in Globally Coupled Phase Oscillators: Noise-Induced Bifurcations, Clustering, and Switching

1997 ◽  
Vol 07 (04) ◽  
pp. 917-922
Author(s):  
Seon Hee Park ◽  
Seunghwan Kim ◽  
Seung Kee Han
Keyword(s):  
Phase Transition ◽  
Noise Intensity ◽  
Multiplicative Noise ◽  
Additive Noise ◽  
Critical Value ◽  
Phase Oscillators ◽  
Deterministic Systems ◽  
Nonequilibrium Phenomena ◽  
Noise Models ◽  
Coupled Phase Oscillators

The Nonequilibrium phenomena in a class of globally coupled phase oscillators systems with multiplicative noise are studied. It is shown that at the critical value of the noise intensity the systems undergo a phase transition and converge to clustered states. We also show that the time delay in the interaction between oscillators gives rise to the switching phenomena of clusters. These phenomena are noise-induced effects which cannot be seen in the deterministic systems or in the simple additive noise models.

scholarly journals Selection of Pairings Reaching Evenly Across the Data (SPREAD): A simple algorithm to design maximally informative fully crossed mating experiments

2014 ◽  
Author(s):  
Kolea Zimmerman ◽  
Daniel Levitis ◽  
Ethan Addicott ◽  
Anne Pringle
Keyword(s):  
Nearest Neighbor ◽  
Simple Algorithm ◽  
Two Dimensional ◽  
Neighbor Distance ◽  
Crossing Experiments ◽  
The Mean ◽  
Parameter Values ◽  
Selection Of ◽  
Novel Algorithm ◽  
Trait Space

We present a novel algorithm for the design of crossing experiments. The algorithm identifies a set of individuals (a ?crossing-set?) from a larger pool of potential crossing-sets by maximizing the diversity of traits of interest, for example, maximizing the range of genetic and geographic distances between individuals included in the crossing-set. To calculate diversity, we use the mean nearest neighbor distance of crosses plotted in trait space. We implement our algorithm on a real dataset ofNeurospora crassastrains, using the genetic and geographic distances between potential crosses as a two-dimensional trait space. In simulated mating experiments, crossing-sets selected by our algorithm provide better estimates of underlying parameter values than randomly chosen crossing-sets.

scholarly journals Applying shadowing technique to improve students' listening achievement

2020 ◽  
Vol 5 (1) ◽  
pp. 47-56
Author(s):  
Fitri Maini ◽  
Rachmanita
Keyword(s):  
Null Hypothesis ◽  
Sampling Method ◽  
Critical Value ◽  
T Test ◽  
Control Group ◽  
Tenth Graders ◽  
Tenth Grade ◽  
Quasi Experimental ◽  
The Mean ◽  
Experimental Group

This study tried find the students’ improvement in listening achievement after having taught by using the shadowing technique. The method used was a quasi-experimental that involved two groups, namely the control group and experimental group. The population of this study was all the tenth graders of SMA Negeri 3 Unggulan Kayuagung with a total number of 198 tenth graders. Purposive sampling method was applied to select the sample involved 72 tenth graders. In collecting the data, try out the test was used to get the desirable questions that would be used in the pretest and posttest to both groups in the control and experimental group. To verify the hypothesis, the normality and homogeneity of the data were firstly analyzed before being continued to be analyzed by using a t-test. Based on the result of data analysis in an independent sample t-test, there were some findings found. First, the mean score of a posttest (75.56) in the experimental group was higher than the pretest (69.03) in the control group. Secondly, the value of tobtained was 2.77 at the significant level of p<0.05 in two-tailed testing with df = 70, the critical value of ttable was 1.99. Since the value of tobtained was higher than ttable, the null hypothesis (Ho) was rejected and the research hypothesis was accepted. In conclusion, it showed that the shadowing technique could improve the tenth-grade students’ listening achievement at SMA Negeri 3 Unggulan Kayuagung.

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