scholarly journals A version of Kac’s lemma on first return times for suspension flows

2016 ◽  
Vol 16 (02) ◽  
pp. 1660002 ◽  
Author(s):  
Paulo Varandas
Keyword(s):  
Probability Measure ◽  
Cross Sections ◽  
Positive Measure ◽  
Return Time ◽  
Suspension Flows ◽  
Classical Version ◽  
Return Times ◽  
Set Relation ◽  
The Mean ◽  
First Return Time

In this paper, we study the mean return times to a given set for suspension flows. In the discrete time setting, this corresponds to the classical version of Kac’s lemma [11] that the mean of the first return time to a set with respect to the normalized probability measure is one. In the case of suspension flows we provide formulas to compute the mean return time. Positive measure sets on cross sections are also considered. In particular, this varies linearly with continuous reparametrizations of the flow and takes into account the mean escaping time from the original set. Relation with entropy and returns to positive measure sets on cross sections is also considered.

Scalings of first-return time for random walks on generalized and weighted transfractal networks

2019 ◽  
Vol 33 (26) ◽  
pp. 1950306
Author(s):  
Qin Liu ◽  
Weigang Sun ◽  
Suyu Liu
Keyword(s):  
Random Walks ◽  
Large Scale ◽  
Probability Generating Function ◽  
Return Time ◽  
Network Size ◽  
Large Network ◽  
Large Scale Network ◽  
Scale Network ◽  
The Mean ◽  
First Return Time

The first-return time (FRT) is an effective measurement of random walks. Presently, it has attracted considerable attention with a focus on its scalings with regard to network size. In this paper, we propose a family of generalized and weighted transfractal networks and obtain the scalings of the FRT for a prescribed initial hub node. By employing the self-similarity of our networks, we calculate the first and second moments of FRT by the probability generating function and obtain the scalings of the mean and variance of FRT with regard to network size. For a large network, the mean FRT scales with the network size at the sublinear rate. Further, the efficiency of random walks relates strongly with the weight factor. The smaller the weight, the better the efficiency bears. Finally, we show that the variance of FRT decreases with more number of initial nodes, implying that our method is more effective for large-scale network size and the estimation of the mean FRT is more reliable.

SCALING PROPERTIES OF FIRST RETURN TIME ON WEIGHTED TRANSFRACTALS (1,3)-FLOWERS

Fractals ◽  
2018 ◽  
Vol 26 (06) ◽  
pp. 1850095 ◽  
Author(s):  
MEIFENG DAI ◽  
HUIJIA CHI ◽  
XIANBIN WU ◽  
YUE ZONG ◽  
WENJING FENG ◽  
...  
Keyword(s):  
Complex Networks ◽  
Real Life ◽  
Probability Generating Function ◽  
Return Time ◽  
Exact Probability ◽  
Scaling Properties ◽  
Mean And Variance ◽  
The Mean ◽  
First Return Time ◽  
The Impact

Complex networks are omnipresent in science and in our real life, and have been the focus of intense interest. It is vital to research the impact of their characters on the dynamic progress occurring on complex networks for weight-dependent walk. In this paper, we first consider the weight-dependent walk on one kind of transfractal (or fractal) which is named the weighted transfractal [Formula: see text]-flowers. And we pay attention to the first return time (FRT). We mainly calculate the mean and variance of FRT for a prescribed hub (i.e. the most concerned nodes) in virtue of exact probability generating function and its properties. Then, we obtain the mean and the secondary moment of the first return time. Finally, using the relationship among the variance, mean and the secondary moment, we obtain the variance of FRT and the scaling properties of the mean and variance of FRT on weighted transfractals [Formula: see text]-flowers.

SCALING OF RETURN TIMES FOR A HIGH-RESOLUTION RAINFALL TIME SERIES

Fractals ◽  
2002 ◽  
Vol 10 (03) ◽  
pp. 285-290 ◽  
Author(s):  
F. SCHMITT ◽  
C. NICOLIS
Keyword(s):  
Time Series ◽  
High Resolution ◽  
Probability Density ◽  
Extreme Events ◽  
Return Time ◽  
Rainfall Time Series ◽  
Large Intensity ◽  
Return Times ◽  
Wide Range ◽  
The Mean

Rainfall is a highly intermittent field over a wide range of time and space scales. We study a high resolution rainfall time series exhibiting large intensity fluctuations and localized events. We consider the return times of a given intensity, and show that the time series composed of these return times is itself also very intermittent, obeying to a hyperbolic probability density, entailing that the mean return time diverges. This is an unexpected property since mean return times are often introduced in meteorology, especially for the study of risk associated to extreme events. It suggests that the intermittency of first return times of extreme events should be taken into account when making statistical predictions.

scholarly journals Aerodynamics of smooth and rough square-section prisms at incidence in very high Reynolds-number cross-flows

2021 ◽  
Vol 62 (3) ◽  
Author(s):  
Nils Paul van Hinsberg
Keyword(s):  
Reynolds Number ◽  
Cross Sections ◽  
Reynolds Numbers ◽  
Circular Cylinders ◽  
Surface Boundary ◽  
Experimental Proof ◽  
Surface Boundary Layer ◽  
Pitch Moment ◽  
The Mean ◽  
High Reynolds

Abstract The aerodynamics of smooth and slightly rough prisms with square cross-sections and sharp edges is investigated through wind tunnel experiments. Mean and fluctuating forces, the mean pitch moment, Strouhal numbers, the mean surface pressures and the mean wake profiles in the mid-span cross-section of the prism are recorded simultaneously for Reynolds numbers between 1$$\times$$ × 10$$^{5}$$ 5 $$\le$$ ≤ Re$$_{D}$$ D $$\le$$ ≤ 1$$\times$$ × 10$$^{7}$$ 7 . For the smooth prism with $$k_s$$ k s /D = 4$$\times$$ × 10$$^{-5}$$ - 5 , tests were performed at three angles of incidence, i.e. $$\alpha$$ α = 0$$^{\circ }$$ ∘ , −22.5$$^{\circ }$$ ∘ and −45$$^{\circ }$$ ∘ , whereas only both “symmetric” angles were studied for its slightly rough counterpart with $$k_s$$ k s /D = 1$$\times$$ × 10$$^{-3}$$ - 3 . First-time experimental proof is given that, within the accuracy of the data, no significant variation with Reynolds number occurs for all mean and fluctuating aerodynamic coefficients of smooth square prisms up to Reynolds numbers as high as $$\mathcal {O}$$ O (10$$^{7}$$ 7 ). This Reynolds-number independent behaviour applies to the Strouhal number and the wake profile as well. In contrast to what is known from square prisms with rounded edges and circular cylinders, an increase in surface roughness height by a factor 25 on the current sharp-edged square prism does not lead to any notable effects on the surface boundary layer and thus on the prism’s aerodynamics. For both prisms, distinct changes in the aerostatics between the various angles of incidence are seen to take place though. Graphic abstract

scholarly journals Extension of Pin-Based Point-Wise Energy Slowing-Down Method for VHTR Fuel with Double Heterogeneity

Energies ◽  
2021 ◽  
Vol 14 (8) ◽  
pp. 2179
Author(s):  
Tae-Young Han ◽  
Jin-Young Cho ◽  
Chang-Keun Jo ◽  
Hyun-Chul Lee
Keyword(s):  
Cross Sections ◽  
Cell Model ◽  
Unit Cell ◽  
Moderation Effect ◽  
Slowing Down ◽  
Matrix Layer ◽  
The Mean ◽  
Dancoff Factor ◽  
Double Heterogeneity ◽  
Very High

For the resonance treatment of a very high temperature reactors (VHTR) fuel with the double heterogeneity, an extension of the pin-based pointwise energy slowing-down method (PSM) was developed and implemented into DeCART. The proposed method, PSM-double heterogeneity (DH), has an improved spherical unit cell model with an explicit tri-structural isotropic (TRISO) model, a matrix layer, and a moderator for reflecting the moderation effect. The moderator volume was analytically derived using the relation of the Dancoff factor and the mean chord length. In the first step, the pointwise homogenized cross-sections for the compact was obtained after solving the slowing down equation for the spherical unit cell. Then, the shielded cross-section for the homogenized fuel compact was generated using the original PSM. The verification calculations were performed for the fuel pins with various packing fractions, compact sizes, TRISO sizes, and fuel temperatures. Additionally, two fuel block problems with very different sizes were examined and the depletion calculation was carried out for investigating the accuracy of the proposed method. They revealed that the PSM-DH has a good performance in the VHTR problems.

Comparison of myocardial T1 mapping during breath-holding and free-breathing

2021 ◽  
pp. 1-5
Author(s):  
Hideharu Oka ◽  
Kouichi Nakau ◽  
Sadahiro Nakagawa ◽  
Yuki Kobayashi ◽  
Rina Imanishi ◽  
...  
Keyword(s):  
Cross Sections ◽  
T1 Mapping ◽  
Free Breathing ◽  
Breath Holding ◽  
Basal Region ◽  
Analysis Method ◽  
Imaging Analysis ◽  
Myocardial T1 ◽  
The Mean ◽  
Almost All

Abstract Background: T1 mapping is a recently developed imaging analysis method that allows quantitative assessment of myocardial T1 values obtained using MRI. In children, MRI is performed under free-breathing. Thus, it is important to know the changes in T1 values between free-breathing and breath-holding. This study aimed to compare the myocardial T1 mapping during breath-holding and free-breathing. Methods: Thirteen patients and eight healthy volunteers underwent cardiac MRI, and T1 values obtained during breath-holding and free-breathing were examined and compared. Statistical differences were determined using the paired t-test. Results: The mean T1 values during breath-holding were 1211.1 ± 39.0 ms, 1209.7 ± 37.4 ms, and 1228.9 ± 52.5 ms in the basal, mid, and apical regions, respectively, while the mean T1 values during free-breathing were 1165.1 ± 69.0 ms, 1103.7 ± 55.8 ms, and 1112.0 ± 81.5 ms in the basal, mid, and apical regions, respectively. The T1 values were lower during free-breathing than during breath-holding in almost all segments (basal: p = 0.008, mid: p < 0.001, apical: p < 0.001). The mean T1 values in each cross section were 3.1, 7.8, and 7.7% lower during free-breathing than during breath-holding in the basal, mid, and apical regions, respectively. Conclusions: We found that myocardial T1 values during free-breathing were about 3–8% lower in all cross sections than those during breath-holding. In free-breathing, it may be difficult to assess myocardial T1 values, except in the basal region, because of underestimation; thus, the findings should be interpreted with caution, especially in children.

scholarly journals Pulse Radiolysis Studies of Collisional Deexcitation of Ne(3P1) by H2

2015 ◽  
Vol 19 (1) ◽  
pp. 75-78
Author(s):  
Deba Bahadur Khadka
Keyword(s):  
Optical Absorption ◽  
Absorption Spectroscopy ◽  
Cross Sections ◽  
Pulse Radiolysis ◽  
Science And Technology ◽  
Optical Absorption Spectroscopy ◽  
Time Resolved ◽  
Collisional Energy ◽  
The Mean ◽  
Collisional Deexcitation

The cross sections for the deexcitation of Ne(3P1) by H2 have been measured as a function of the mean collisional energy in the range of 17.3-37.9 meV or in the temperature range from 134 K to 293 K using a pulse radiolysis method as combined with time-resolved optical absorption spectroscopy. The deexcitation cross sections are in the range of 2.1- 5.6 Å2 for Ne(3P1) and nearly constant or increase slightly with increasing the collisional energy.Journal of Institute of Science and Technology, 2014, 19(1): 75-78

scholarly journals Seasonal and annual mass balances of Mera and Pokalde glaciers (Nepal Himalaya) since 2007

2013 ◽  
Vol 7 (4) ◽  
pp. 3337-3378 ◽  
Author(s):  
P. Wagnon ◽  
C. Vincent ◽  
Y. Arnaud ◽  
E. Berthier ◽  
E. Vuillermoz ◽  
...  
Keyword(s):  
Mass Balance ◽  
Cross Sections ◽  
Mass Balances ◽  
Equilibrium Line Altitude ◽  
Nepal Himalaya ◽  
Limited Mass ◽  
In Situ Observations ◽  
The Mean ◽  
Southern Flank

Abstract. In the Everest region, Nepal, ground-based monitoring programs were started on the debris-free Mera Glacier (27.7° N, 86.9° E; 5.1 km2, 6420 to 4940 m a.s.l.) in 2007 and on the small Pokalde Glacier (27.9° N, 86.8° E; 0.1 km2, 5690 to 5430 m a.s.l., ∼ 25 km North of Mera Glacier) in 2009. These glaciers lie on the southern flank of the central Himalaya under the direct influence of the Indian monsoon and receive more than 80% of their annual precipitation in summer (June to September). Despite a large inter-annual variability with glacier-wide mass balances ranging from −0.77± 0.40 m w.e. in 2011–2012 (Equilibrium-line altitude (ELA) at ∼ 6055 m a.s.l.) to + 0.46 ± 0.40 m w.e. in 2010–2011 (ELA at ∼ 5340 m a.s.l.), Mera Glacier has been shrinking at a moderate mass balance rate of −0.10± 0.40 m w.e. yr−1 since 2007. Ice fluxes measured at two distinct transverse cross sections at ∼ 5350 m a.s.l. and ∼ 5520 m a.s.l. confirm that the mean state of this glacier over the last one or two decades corresponds to a limited mass loss, in agreement with remotely-sensed region-wide mass balances of the Everest area. Seasonal mass balance measurements show that ablation and accumulation are concomitant in summer which in turn is the key season controlling the annual glacier-wide mass balance. Unexpectedly, ablation occurs at all elevations in winter due to wind erosion and sublimation, with remobilized snow likely being sublimated in the atmosphere. Between 2009 and 2012, the small Pokalde Glacier lost mass more rapidly than Mera Glacier with respective mean glacier-wide mass balances of −0.72 and −0.26 ± 0.40 m w.e. yr−1. Low-elevation glaciers, such as Pokalde Glacier, have been usually preferred for in-situ observations in Nepal and more generally in the Himalayas, which may explain why compilations of ground-based mass balances are biased toward negative values compared with the regional mean under the present-day climate.

scholarly journals Quantitative Ausmessung des Brom-Affinitätskontinuums und Bestimmung der Detachment-und Attachment-Querschnitte

1970 ◽  
Vol 25 (11) ◽  
pp. 1617-1626 ◽  
Author(s):  
H. Frank ◽  
M. Neiger ◽  
H.-P. Popp
Keyword(s):  
Cross Section ◽  
Cross Sections ◽  
Electron Affinity ◽  
Elastic Cross Section ◽  
Electron Atom ◽  
Intensity Measurements ◽  
Long Wave ◽  
The Mean ◽  
Intense Electron

Abstract A wall stabilized low-current cylindric arc was used to produce the radiation of the negative Bromine-ions. The radiation consists of an affinity-continuum with a long-wave threshold of 3682 Å, yielding an electron affinity for Bromine of 3.366 eV, and of an intense electron-atom Bremsstrahlung in the visible. Intensity measurements of the continua allow the determination of the photo-detachment-and attachment-cross-sections of Bromine and also the determination of the mean elastic cross-section of electrons against Bromine atoms.

Sign in / Sign up

Export Citation Format

Share Document