Probability Distribution Of Energy Research Articles

Risk-averse stochastic unit commitment with incomplete information

ABSTRACTDue to the sustainable nature and stimulus plans from government, renewable energy (such as wind and solar) has been increasingly used in power systems. However, the intermittency of renewable energy creates challenges for power system operators to keep the systems reliable and cost-effective. In addition, information about renewable energy is usually incomplete. Instead of knowing the true probability distribution of the renewable energy course, only a set of historical data samples can be collected from the true (while ambiguous) distribution. In this article, we study two risk-averse stochastic unit commitment models with incomplete information: the first model being a chance-constrained unit commitment model and the second one a two-stage stochastic unit commitment model with recourse. Based on historical data on renewable energy, we construct a confidence set for the probability distribution of the renewable energy and propose data-driven stochastic unit commitment models to hedge against the incomplete nature of the information. Our models also ensure that, with a high probability, a large portion of renewable energy is utilized. Furthermore, we develop solution approaches to solve the models based on deriving strong valid inequalities and Benders’ decomposition algorithms. We show that the risk-averse behavior of both models decreases as more data samples are collected and eventually vanishes as the sample size goes to infinity. Finally, our case studies verify the effectiveness of our proposed models and solution approaches.

Is there substructure around M87?

We present a general method to identify infalling substructure in discrete datasets with position and line-of-sight velocity data. We exploit the fact that galaxies falling onto a brightest cluster galaxy (BCG) in a virialised cluster, or dwarf satellites falling onto a central galaxy like the Milky Way, follow nearly radial orbits. If the orbits are exactly radial, we show how to find the probability distribution for a satellite's energy, given a tracer density for the satellite population, by solving an Abel integral equation. This is an extension of Eddington (1916)'s classical formula for the isotropic distribution function. When applied to a system of galaxies, clustering in energy space can then be quantified using the Kullback-Leibler divergence, and groups of objects can be identified which, though separated in the sky, may be falling in on the same orbit. This method is tested using mock data and applied to the satellite galaxy population around M87, the BCG in Virgo, and a number of associations are found which may represent infalling galaxy groups.

Probability distributions for directed polymers in random media with correlated noise.

The probability distribution for the free energy of directed polymers in random media (DPRM) with uncorrelated noise in d=1+1 dimensions satisfies the Tracy-Widom distribution. We inquire if and how this universal distribution is modified in the presence of spatially correlated noise. The width of the distribution scales as the DPRM length to an exponent β, in good (but not full) agreement with previous renormalization group and numerical results. The scaled probability is well described by the Tracy-Widom form for uncorrelated noise, but becomes symmetric with increasing correlation exponent. We thus find a class of distributions that continuously interpolates between Tracy-Widom and Gaussian forms.

Quantum statistical ensemble for emissive correlated systems.

Relaxation dynamics of complex quantum systems with strong interactions towards the steady state is a fundamental problem in statistical mechanics. The steady state of subsystems weakly interacting with their environment is described by the canonical ensemble which assumes the probability distribution for energy to be of the Boltzmann form. The emergence of this probability distribution is ensured by the detailed balance of the transitions induced by the interaction with the environment. Here we consider relaxation of an open correlated quantum system brought into contact with a reservoir in the vacuum state. We refer to such a system as emissive since particles irreversibly evaporate into the vacuum. The steady state of the system is a statistical mixture of the stable eigenstates. We found that, despite the absence of the detailed balance, the stationary probability distribution over these eigenstates is of the Boltzmann form in each N-particle sector. A quantum statistical ensemble corresponding to the steady state is characterized by different temperatures in the different sectors, in contrast to the Gibbs ensemble. We investigate the transition rates between the eigenstates to understand the emergence of the Boltzmann distribution and find their exponential dependence on the transition energy. We argue that this property of transition rates is generic for a wide class of emissive quantum many-body systems.

Arc erosion behavior of La-doping titanium-zirconium-molybdenum alloy

La-doping titanium-zirconium-molybdenum alloys have good arc erosion resistance performances, but there is no research about the changes during the arc erosion. Arc erosion characteristics of La-doping titanium-zirconium-molybdenum alloys after 5000 operations under direct current 20 V, 15 A and resistive load conditions were investigated using a JF04C test system. The results indicated that the probability distribution and change trend of arc energy and arc time during 5000 operations were similar and the relationship between arc time and arc energy followed exponential function. The change of arc energy with test number was consistent to electrical resistance. Oxide particles, crater and cracks defects were discovered on the surface of La-doping titanium-zirconium-molybdenum alloy. The electrical resistance change is mainly concerned with the surface.

Effect of partial mining of shaft protection pillar in terms of reliability index

ABSTRACTThe work presents calculations of shaft support reliability index during partial extraction of protection pillar deposit and the related seismic phenomena. It has been assumed that the probability of failure caused by seismic phenomena depends on the velocity random variable of the shaft support vibrations. The random vibration velocity is a function of random variables of energy, shock distance and vibration frequency. Estimations of probability distributions for energy and frequency have been based on the actual measurement data from a mine. Failure probability has been estimated by means of methods based on so-called Hasofer-Lind reliability index β.

Arc erosion behavior of Ag/Ni electrical contact materials

Ag/Ni electrical contact materials tend to be weld together under high current and/or high temperature, which was a key problem to restrict the usage of Ag/Ni electric contact materials. Arc erosion characteristics of Ag/12Ni electrical contact material after 50,000 operations under direct current 19 V, 20 A and resistive load conditions were investigated. The result indicated that the probability distribution and change trend of arc energy and arc time during 50,000 operations were similar and the relationship between arc time and arc energy followed exponential function. On the one hand, “Crater” type erosion pit, island-like melted silver, pore, crack and coral-like structure spitting were observed on erosion surface of Ag/Ni contact materials. On the other hand, distribution of Ag and Ni element on molten pool of movable contact was different from that of stationary contact. For movable contact, element Ni mainly distributed on melted pool root, whereas element Ag mainly distributed inside of melted pool. For stationary contact, however, element Ni and Ag distributed layer by layer. Furthermore, arc erosion of stationary contact is more serious than that of movable contact.

Oscillatory Shannon entropy in the process of equilibration of nonequilibrium crystalline systems

We present a study of the equilibration process of some nonequilibrium crystalline systems by means of molecular dynamics simulation technique. The nonequilibrium conditions are achieved in the systems by randomly defining velocity components of the constituent atoms. The calculated Shannon entropy from the probability distribution of the kinetic energy among the atoms at different instants during the process of equilibration shows oscillation as the system relaxes towards equilibrium. Fourier transformations of these oscillating Shannon entropies reveal the existence of Debye frequency of the concerned system.

Jerky magnetic noises generated by cyclic deformation of martensite in Ni2MnGa single crystalline shape memory alloys

It is shown that during periodic deformation of martensitic Ni2MnGa single crystalline alloy jerky magnetic noises are emitted. Above a threshold limit in the deformation amplitude, the noise energy per deformation cycle showed increasing tendency with increasing deformation. Energy and amplitude probability distributions of the noise were characterized by power law functions. The energy exponents were independent of the deformation amplitude in the investigated range. The decrease of the noise energy as well as power exponents with increasing magnetic field was interpreted by the decrease of the multiplicity of the martensite variants.

Deterioration of FRP-Concrete Interface under the Environment of Dry-Wet Cycling at High Temperature Based on Reliability Theory

Five conventional tests (Shapiro-Wilk test, Kolmogorov-Smirnov test, Cramer-von Mises test, Anderson-Darling test and Chi-Square test) were carried out in this paper to learn the probability distribution of fracture energy of FRP-concrete interface under the environment of dry-wet cycling at high temperature. The relationship between interfacial fracture energy and the number of cycles was established through nonlinear regression analysis. Then the reliability index and the probability of deterioration of FRP-concrete interface that uses experimental data as design values were analyzed according to the reliability theory. It is shown that the optimum distribution of interfacial fracture energy is lognormal distribution, and the relationship between logarithmic mean value of interfacial fracture energy and number of cycles is subject to the exponential function. As the cycle number increases, reliability index decreases rapidly while the probability of deterioration the other way around in the beginning, yet both are stabilized at a certain level eventually. The probability of deterioration has reached a high value in a few cycles in experiments.

Conformational transitions of a weak polyampholyte.

Using grand canonical Monte Carlo simulations of a flexible polyelectrolyte where the charges are in contact with a reservoir of constant chemical potential given by the solution pH, we study the behavior of weak polyelectrolytes in poor and good solvent conditions for polymer backbone. We address the titration behavior and conformational properties of a flexible diblock polyampholyte chain formed of two oppositely charged weak polyelectrolyte blocks, each containing equal number of identical monomers. The change of solution pH induces charge asymmetry in a diblock polyampholyte. For diblock polyampholyte chains in poor solvents, we demonstrate that a discontinuous transition between extended (tadpole) and collapsed (globular) conformational states is attainable by varying the solution pH. The double-minima structure in the probability distribution of the free energy provides direct evidence for the first-order like nature of this transition. At the isoelectric point electrostatically driven coil-globule transition of diblock polyampholytes in good solvents is found to consist of different regimes identified with increasing electrostatic interaction strength. At pH values above or below the isoelectric point diblock chains are found to have polyelectrolyte-like behavior due to repulsion between uncompensated charges along the chain.

Protein folding thermodynamics: a new computational approach.

Folding free energy is the fundamental thermodynamic quantity characterizing the stability of a protein. Yet, its accurate determination based on computational techniques remains a challenge in physical chemistry. A straightforward brute-force approach would be to conduct molecular dynamics simulations and to estimate the folding free energy from the equilibrium population ratio of the unfolded and folded states. However, this approach is not sensible at physiological conditions where the equilibrium population ratio is vanishingly small: it is extremely difficult to reliably obtain such a small equilibrium population ratio due to the low rate of folding/unfolding transitions. It is therefore desirable to have a computational method that solely relies on simulations independently carried out for the folded and unfolded states. Here, we present such an approach that focuses on the probability distributions of the effective energy (solvent-averaged protein potential energy) in the folded and unfolded states. We construct these probability distributions for the protein villin headpiece subdomain by performing extensive molecular dynamics simulations and carrying out solvation free energy calculations. We find that the probability distributions of the effective energy are well-described by the Gaussian distributions for both the folded and unfolded states due to the central limit theorem, which enables us to calculate the protein folding free energy in terms of the mean and the width of the distributions. The computed protein folding free energy (-2.5 kcal/mol) is in accord with the experimental result (ranging from -2.3 to -3.2 kcal/mol depending on the experimental methods).

Endpiont Detection in Noisy Speech Signal Using Teager Energy Entropy

In this paper, we propose a new method using teager energy operator and entropy to solve endpoint detection problem in noisy environment. With the teager energy operator, it is sensitive on AM and FM signal and noise suppression capability on noisy speech signal, calculate teager energy of noisy speech signal. According to the different teager energy probability distribution between noise and speech signal, teager energy entropy is different. Set two soft thresholds of four states to detect the endpoint of noisy speech signal. The simulation shows that the method has good effect of endpoint detection in low SNR conditions, the simulation results show that teager energy entropy of speech signal endpoint detection in noisy environments is feasible and effective, and improves the reliability of endpoint detection.

Critical energy distribution function of the Baxter–Wu model

In this work we examine the critical finite-size scaling behavior of the energy probability distribution function and its corresponding Binder cumulant at critical point. Based on the results of Monte Carlo simulations at zero external magnetic field using the recently developed triangle-cluster algorithm, we calculate the energy distribution function’s exponents and we derive the scaling relations for the energy Binder cumulant. Finally, we predict the exact form of the scaled energy distribution function. Most of our conclusions seem applicable not only to the Baxter–Wu model but also to other Ising-like models.

Insight into lithium distribution in lithium-stuffed garnet oxides through neutron diffraction and atomistic simulation: Li 7-x La 3 Zr 2-x Ta x O 12 (x = 0–2) series

Abstract Lithium-stuffed garnet oxides are promising candidates of lithium ion electrolyte materials due to their high ionic conductivities and good chemical stability. In this study, time-of-flight (TOF) neutron diffraction experiments and the Rietveld refinement were performed on four garnet compounds in the Li 7-x La 3 Zr 2-x Ta x O 12 (x = 0–2) series to study their average structures. Different structural models (split-site and anisotropic displacement) for lithium disorder at tetrahedral (Td) and octahedral (Oh) sites were compared and results suggested possible lithium disorder around both ideal Oh and ideal Td sites. To study the local lithium distribution, atomistic simulations based on static energy minimization with interatomic potentials were carried out on a large number of configurations of eight compositions. We demonstrated that energy probability distribution plots were helpful in understanding the lithium disorder/order in these materials. Nuclear density maps provided a visual presentation of structural disorder at both Td and Oh lithium sites. Our simulation results suggested that Td lithium occupancy is generally lower than that obtained from the average structure (Rietveld refinement) and the exclusion principle (no nearest-neighbor Td–Oh–Td lithium triplets). In addition, the nearest-neighbor Td–Oh lithium pairs and (Oh,□)–Td–(Oh,□) lithium clusters appear to be the characteristic local features contributing to the structure and conduction of these lithium-stuffed garnet oxides.

Quantum quench in the Luttinger model with finite temperature initial state

We study the non-equilibrium dynamics of the Luttinger model after a quantum quench, when the initial state is a finite temperature thermal equilibrium state. The diagonal elements of the density matrix in the steady state show thermal features for high temperature initial states only, otherwise retain highly non-thermal character. The time evolution of Uhlmann fidelity, which measures the distance between the time evolved and initial states, is evaluated for arbitrary initial temperatures and quench protocols. In the long time limit, the overlap between the time evolved and initial system decreases exponentially with the temperature with a universal prefactor. Within perturbation theory, the statistics of final total energy and work are numerically evaluated in the case of a sudden quench, which yield identical distributions at zero temperature. In both statistics, temperature effects are more significant in small systems. The Dirac-delta peak at the adiabatic ground state energy remains present in the probability distribution of the total energy, but disappears from the work distribution at non-zero initial temperatures.

Probability distribution for energy of saturated broadband ocean acoustic transmission: Results from Gulf of Maine 2006 experiment

The probability distribution of ocean-acoustic broadband signal energy after saturated multipath propagation is derived using coherence theory. The frequency components obtained from Fourier decomposition of a broadband signal are each assumed to be fully saturated with energy spectral density that obey the exponential distribution with 5.6 dB standard deviation and unity scintillation index. When the signal bandwidth and measurement time are larger than the correlation bandwidth and correlation time respectively of its energy spectral density components, the broadband signal energy obtained by integrating the energy spectral density across the signal bandwidth then follows the Gamma distribution with standard deviation smaller than 5.6 dB and scintillation index less than unity. The theory is verified with broadband transmissions in the Gulf of Maine shallow water waveguide in the 300–1200 Hz frequency range. The standard deviations of received broadband signal energies range from 2.7 to 4.6 dB for effective bandwidths up to 42 Hz, while the standard deviations of individual energy spectral density components are roughly 5.6 dB. The energy spectral density correlation bandwidths of the received broadband signals are found to be larger for signals with higher center frequencies and are roughly 10% of each center frequency.

Lineal energy and radiation quality in radiation therapy: model calculations and comparison with experiment

Microdosimetry is a recommended method for characterizing radiation quality in situations when the biological effectiveness under test is not well known. In such situations, the radiation beams are described by their lineal energy probability distributions. Results from radiobiological investigations in the beams are then used to establish response functions that relate the lineal energy to the relative biological effectiveness (RBE). In this paper we present the influence of the size of the simulated volume on the relation to the clinical RBE values (or weighting factors). A single event probability distribution of the lineal energy is approximated by its dose average lineal energy () which can be measured or calculated for volumes from a few micrometres down to a few nanometres. The clinical RBE values were approximated as the ratio of the α-values derived from the LQ-relation. Model calculations are presented and discussed for the SOBP of a 12C ion (290 MeV u−1) and the reference 60Co γ therapy beam. Results were compared with those for a conventional x-ray therapy beam, a 290 MeV proton beam and a neutron therapy beam. It is concluded that for a simulated volume of about 10 nm, the α-ratio increases approximately linearly with the -ratio for all the investigated beams. The correlation between y and α provides the evidence to characterize a radiation therapy beam by the lineal energy when, for instance, weighting factors are to be estimated.

Statistical and polarization properties of giant pulses of the millisecond pulsar B1937+21

We have studied the statistical and polarization properties of giant pulses (GPs) emitted by the millisecond pulsar B1937+21, with high sensitivity and time resolution. The observations were made in June 2005 with the 100-m Robert C. Byrd Green Bank Telescope at S-band (2052-2116 MHz) using the Mk5A VLBI recording system, with formal time resolution of 16 ns. The total observing time was about 4.5 hours; the rate of detection of GPs was about 130 per hour at the average longitudes of the main pulse (MPGPs) and 60 per hour at the interpulse (IPGPs). While the average profile shows well-defined polarization behavior, with regular evolution of the linear polarization position angle (PA), GPs exhibit random properties, occasionally having high linear or circular polarization. Neither MPGPs nor IPGPs show a preferred PA. The cumulative probability distribution (CPD) of GP pulse energy was constructed down to the level where GPs merge with regular pulses and noise. For both MPGPs and IPGPs, the CPD follows a power law with a break, the power index changing from -2.4 at high energy to -1.6 for low energy. Pulse smearing due to scattering masks the intrinsic shape and duration of the detected GPs. The smearing time varied during the observing session within a range of a few hundred nanoseconds. The measured polarization and statistical properties of GPs impose strong constraints on physical models of GPs. Some of these properties support a model in which GPs are generated by the electric discharge caused by magnetic reconnection of field lines connecting the opposite magnetic poles of a neutron star.

에드 혹 네트워크에서 최적 경로의 유효성 있는 클러스터링 알고리즘에 관한 연구

본 논문에서는 노드의 위치 정보와 유효성 경로에 따라 클러스터링내의 헤드 노드를 선출하는 방법 중 하나로 에너지 효율성을 고려한 ECOPS(Energy Conserving Optimal path Schedule) 알고리즘을 제안한다. 기존 LEACH 알고리즘은 헤드 노드를 선출할 때 노드의 에너지 확률적 분포 함수에 기반 하여 헤드 노드의 주기를 선택적으로 관리하게 된다. 그러나 이 경우 중계노드의 거리 정보 등 상황 정보 인자가 반영되지 않아 위치적으로 또는 중계노드로 적당하지 않은 노드들이 확률분포에 포함되어 헤드노드로 선택 되는 경우가 발생한다. 따라서 본 논문에서는 기존의 LEACH 기반에서 계층적인 클러스터 구조의 토폴로지로부터 헤드 노드를 선택함에 있어 인접한 노드와의 위치상황 정보인자 및 잔존에너지의 상황정보를 이용하는 ECOPS 알고리즘을 제안 한다. 제안된 ECOPS 알고리즘은 헤드 노드 교체 상황에서 후보 헤드노드 중 최적의 효율적인 에너지 보존 경로를 가지는 멤버 노드가 새로운 헤드노드로 선출됨으로써 전체 노드 수명 및 네트워크의 관리를 향상시키는 것으로 모의실험 결과를 나타내었다. In this paper, we introduce a method that can be used to select the position of head node for context-awareness information. The validity of the head node optimal location is saving the energy in the path according to the clustering. It is important how to elect one of the relay node for energy efficiency routing. Existing LEACH algorithm to elect the head node when the node's energy probability distribution function based on the management of the head node is optional cycle. However, in this case, the distance of the relay node status information including context-awareness parameters does not reflect. These factors are not suitable for the relay node or nodes are included in the probability distribution during the head node selects occurs. In particular, to solve the problems from the LEACH-based hierarchical clustering algorithms, this study defines location with the status context information and the residual energy factor in choosing topology of the structure adjacent nodes. The proposed ECOPS (Energy Conserving Optimal path Schedule) algorithm that contextual information is contributed for head node selection in topology protocols. This proposed algorithm has the head node replacement situations from the candidate head node in the optimal path and efficient energy conservation that is the path of the member nodes. The new head node election technique show improving the entire node lifetime and network in management the network from simulation results.