scholarly journals Planting Colourings Silently

2016 ◽  
Vol 26 (3) ◽  
pp. 338-366 ◽  
Author(s):  
VICTOR BAPST ◽  
AMIN COJA-OGHLAN ◽  
CHARILAOS EFTHYMIOU
Keyword(s):  
Phase Transition ◽  
Random Graph ◽  
Random Variable ◽  
Average Degree ◽  
Fixed Integer ◽  
Wide Range ◽  
Concentration Result

Letk⩾ 3 be a fixed integer and letZk(G) be the number ofk-colourings of the graphG. For certain values of the average degree, the random variableZk(G(n,m)) is known to be concentrated in the sense that$\tfrac{1}{n}(\ln Z_k(G(n,m))-\ln\Erw[Z_k(G(n,m))])$converges to 0 in probability (Achlioptas and Coja-Oghlan,Proc. FOCS 2008). In the present paper we prove a significantly stronger concentration result. Namely, we show that for a wide range of average degrees,$\tfrac{1}{\omega}(\ln Z_k(G(n,m))-\ln\Erw[Z_k(G(n,m))])$converges to 0 in probability foranydiverging function$\omega=\omega(n)\ra\infty$. Forkexceeding a certain constantk0this result covers all average degrees up to the so-calledcondensation phase transitiondk,con, and this is best possible. As an application, we show that the experiment of choosing ak-colouring of the random graphG(n,m) uniformly at random is contiguous with respect to the so-called ‘planted model’.

scholarly journals On the Number of Solutions in Random Graphk-Colouring

2018 ◽  
Vol 28 (1) ◽  
pp. 130-158 ◽  
Author(s):  
FELICIA RASSMANN
Keyword(s):  
Phase Transition ◽  
Asymptotic Distribution ◽  
Random Graph ◽  
Number Of Solutions ◽  
Fixed Integer ◽  
Wide Range

Letk⩾ 3 be a fixed integer. We exactly determine the asymptotic distribution of lnZk(G(n, m)), whereZk(G(n, m)) is the number ofk-colourings of the random graphG(n, m). A crucial observation to this end is that the fluctuations in the number of colourings can be attributed to the fluctuations in the number of small cycles inG(n, m). Our result holds for a wide range of average degrees, and forkexceeding a certain constantk0it covers all average degrees up to the so-calledcondensation phase transition.

scholarly journals The Diameter of Sparse Random Graphs

2010 ◽  
Vol 19 (5-6) ◽  
pp. 835-926 ◽  
Author(s):  
OLIVER RIORDAN ◽  
NICHOLAS WORMALD
Keyword(s):  
Phase Transition ◽  
Random Graph ◽  
Branching Process ◽  
Correction Term ◽  
Separate Analysis ◽  
Wide Range ◽  
Range Of Functions ◽  
Finite Distance ◽  
Additive Correction

In this paper we study the diameter of the random graph G(n, p), i.e., the largest finite distance between two vertices, for a wide range of functions p = p(n). For p = λ/n with λ > 1 constant we give a simple proof of an essentially best possible result, with an Op(1) additive correction term. Using similar techniques, we establish two-point concentration in the case that np → ∞. For p =(1 + ε)/n with ε → 0, we obtain a corresponding result that applies all the way down to the scaling window of the phase transition, with an Op(1/ε) additive correction term whose (appropriately scaled) limiting distribution we describe. Combined with earlier results, our new results complete the determination of the diameter of the random graph G(n, p) to an accuracy of the order of its standard deviation (or better), for all functions p = p(n). Throughout we use branching process methods, rather than the more common approach of separate analysis of the 2-core and the trees attached to it.

Fabrication of nanocrystalline λ-Ti3O5with tunable terahertz wave transmission properties across a temperature induced phase transition

2016 ◽  
Vol 4 (43) ◽  
pp. 10279-10285 ◽  
Author(s):  
Qiwu Shi ◽  
Guoqing Chai ◽  
Wanxia Huang ◽  
Yanli Shi ◽  
Bo Huang ◽  
...  
Keyword(s):  
Phase Transition ◽  
Carbothermal Reduction ◽  
Terahertz Wave ◽  
Wave Transmission ◽  
Slow Phase ◽  
Dynamic Tuning ◽  
Transmission Properties ◽  
Wide Range

Nanocrystalline λ-Ti3O5was fabricated by carbothermal reduction of nano-TiO2. It exhibits a continuous and slow phase transition across a wide range of temperatures, which can lead to dynamic tuning of THz transmission.

scholarly journals On Exact Sampling of Nonnegative Infinitely Divisible Random Variables

2012 ◽  
Vol 44 (3) ◽  
pp. 842-873 ◽  
Author(s):  
Zhiyi Chi
Keyword(s):  
Basic Result ◽  
Random Variables ◽  
Random Variable ◽  
Fixed Number ◽  
Rejection Sampling ◽  
Infinitely Divisible ◽  
Exact Sampling ◽  
Special Cases ◽  
Wide Range ◽  
Lévy Density

Nonnegative infinitely divisible (i.d.) random variables form an important class of random variables. However, when this type of random variable is specified via Lévy densities that have infinite integrals on (0, ∞), except for some special cases, exact sampling is unknown. We present a method that can sample a rather wide range of such i.d. random variables. A basic result is that, for any nonnegative i.d. random variable X with its Lévy density explicitly specified, if its distribution conditional on X ≤ r can be sampled exactly, where r > 0 is any fixed number, then X can be sampled exactly using rejection sampling, without knowing the explicit expression of the density of X. We show that variations of the result can be used to sample various nonnegative i.d. random variables.

scholarly journals ДОСЛІДЖЕННЯ ПОКАЗНИКА ЕФЕКТИВНОСТІ ЕКСПЛУАТАЦІЇ ЗАСОБІВ ВИМІРЮВАЛЬНОЇ ТЕХНІКИ МЕТОДОМ КОМПʼЮТЕРНОГО МОДЕЛЮВАННЯ

2020 ◽  
pp. 166-169
Author(s):  
Олександр Володимирович Томашевський ◽  
Геннадій Валентинович Сніжной
Keyword(s):  
Computer Simulation ◽  
Distribution Function ◽  
Normal Distribution ◽  
Failure Rate ◽  
Random Variable ◽  
Operational Efficiency ◽  
Distribution Law ◽  
Maintenance System ◽  
Wide Range ◽  
Calibration Interval

The operational efficiency of measuring equipment (ME) is important in determining the cost of maintaining ME. To characterize the operational efficiency of the ME, an efficiency indicator has been introduced, an increase of which will reduce costs caused by the release of defective products due to the use of ME with unreliable indications. Over time, the ME parameters change under the influence of external factors and the ME aging processes inevitably occur, as a result of which the parameters of the ME metrological service system change. Therefore, in the general case, the parameters of the metrological maintenance system of ME should be considered as random variables. Accordingly, the efficiency indicator of measuring instruments is also a random variable, for the determination of which it is advisable to apply the methods of mathematical statistics and computer simulation. The performance indicator depends on the parameters of the metrological maintenance ME system, such as the calibration interval, the time spent by the ME on metrological maintenance, and the likelihood of ME failure-free operation. As a random variable, the efficiency indicator has a certain distribution function. To determine the distribution function of the efficiency indicator and the corresponding statistical characteristics, a computer simulation method was used. A study was made of the influence on the indicator of the effectiveness of the parameters of the metrological maintenance system ME (interesting interval, the failure rate of ME). The value of the verification interval and the failure rate of MEs varied over a wide range typical of real production. The time spent by ME on metrological services is considered as a random variable with a normal distribution law. To obtain random numbers with a normal distribution law, the Box-Muller method is used. After modeling, the statistical processing of the obtained results was done. It is shown that in real production, the efficiency indicator has a normal distribution law and the value of the efficiency indicator with an increase in the calibration interval does not practically change.

scholarly journals Effect of Sintering Temperature on Metal-Insulator Phase Transition in La1-xCaxMnO3 Perovskites

2020 ◽  
Vol 2 (1) ◽  
pp. 37-42
Author(s):  
Arunachalam M ◽  
Thamilmaran P ◽  
Sakthipandi K
Keyword(s):  
Phase Transition ◽  
Bulk Modulus ◽  
Sintering Temperature ◽  
Magnetic Sensors ◽  
Temperature Dependent ◽  
Metal Insulator ◽  
Wide Range ◽  
Different Temperatures ◽  
Insulator Phase Transition

Lanthanum calcium based perovskites are found to be advantageous for the possible applications in magnetic sensors/reading heads, cathodes in solid oxide fuel cells, and frequency switching devices. In the present investigation La0.3Ca0.7MnO3 perovskites were synthesised through solid state reaction and sintered at four different temperatures such as 900, 1000, 1100 and 1200˚ C. X-ray powder diffraction pattern confirms that the prepared La0.3Ca0.7MnO3 perovskites have orthorhombic structure with Pnma space group. Ultrasonic in-situ measurements have been carried out on the La0.3Ca0.7MnO3 perovskites over wide range of temperature and elastic constants such as bulk modulus of the prepared La0.3Ca0.7MnO3 perovskites was obtained as function of temperature. The temperature-dependent bulk modulus has shown an interesting anomaly at the metal-insulator phase transition. The metal insulator transition temperature derived from temperature-dependent bulk modulus increases from temperature 352˚ C to 367˚ C with the increase of sintering temperature from 900 to 1200˚ C.

scholarly journals Ударно-волновой полиморфный переход в пористом графите

2021 ◽  
Vol 91 (11) ◽  
pp. 1707
Author(s):  
С.А. Кинеловский
Keyword(s):  
Phase Transition ◽  
Shock Wave ◽  
Elastic Energy ◽  
Polymorphic Transformation ◽  
Polymorphic Transition ◽  
Initial Structure ◽  
Graphite Phase ◽  
Proposed Model ◽  
Porous Graphite ◽  
Wide Range

For the polymorphic transformation of porous graphite in the shock, the previously proposed model linking the process of graphite phase transition with a change in the elastic energy of a substance has been tested. It is shown that the model plausibly describes the experimental results outside the transition zone in a fairly wide range of changes in the porosity of samples with their different initial structure. It is discussed how the model under consideration changes the currently existing ideas about the thermodynamics of the polymorphic transition of matter in a shock wave.

Photocontrol of a dynamic phase transition in the CDW state

2002 ◽  
Vol 12 (9) ◽  
pp. 297-301
Author(s):  
K. Miyano ◽  
N. Ogawa
Keyword(s):  
Phase Transition ◽  
Internal Stress ◽  
One Dimensional ◽  
Dynamic Phase ◽  
Wide Range ◽  
Dynamic Phase Transition

A strong photoinduced suppression of the creep to slide dynamic phase transition was discovered in a quasi one-dimensional CDW material, K0.3MoO3. It is manifested in hysteretic “photoresistivity", an increase in the resistance by orders of magnitude under the illumination of light of modest intensity. Based on a wide range of measurements, it is concluded that the effect is due to the release of the internal stress by photoexcited jumps of the CDW phase over pinning sites: a phenomenon which can be effective only in a system, in which the thermally excited quasiparticles are negligibly small and hence the `bare' CDW properties emerge.

scholarly journals Dielectric Phase Transition Behaviour Study of Dry Route Derived (BA0.5 SN0.5) TIO3 Ceramics

2019 ◽  
Vol 40 ◽  
pp. 73-77
Author(s):  
Bhojraj Bhandari ◽  
Bhadra Prasad Pokheral
Keyword(s):  
Phase Transition ◽  
Barium Titanate ◽  
Content Volume ◽  
Ceramic Materials ◽  
Hydraulic Press ◽  
Binary Solid Solution ◽  
Sensor Material ◽  
Wide Range ◽  
Free Environment ◽  
Liquid Displacement

Ceramic materials display a wide range of properties that facilitate their use in many different product areas. Currently, there has been keen interest in the field of ceramic materials due to their excellent mechanical and physical properties. Barium Stannate Titanate (BST) is a binary solid solution system composed of ferroelectric Barium titanate and non-ferroelectric barium titanate. In this study, the phase transition behavior of (Ba1-xSnx)TiO3 (x = 0.5) (BST) ceramics  was obtained by the dry-route method. The previous studies were based on Sn 2+ on the Ti site with varying values of x. The powders after calcination are compacted in the form of pellets using a hydraulic press at an optimized load above 70KN. The experimental density of our sample measured by liquid displacement method with glycerin was lower than theoretical density, giving the shape is highly dense with low porosity. The structure shows that on increasing the Sn2+ content volume decreases due to the size of Sn2+, which is smaller than that of Ba2+, in comparison to BaTiO3. As the demand of lead-free environment-friendly sensor is increasing, thus obtained BST has great applications as a sensor material in modern electronic devices.

Sign in / Sign up

Export Citation Format

Share Document