Note on islands in path-length sequences of binary trees

An earlier characterization of topologically ordered (lexicographic) path-length sequences of binary trees is reformulated in terms of an integrality condition on a scaled Kraft sum of certain subsequences (full segments, or islands). The scaled Kraft sum is seen to count the set of ancestors at a certain level of a set of topologically consecutive leaves is a binary tree.Comment: 4 page

Site Location Determination Using Geographic Information Systems: The Process and a Case Study

In this study, we developed a five-step process for GIS-enabled site location determination in different domains. We applied that process to a real case study to examine its feasibility. The case was about determination of a suitable location for a children-oriented store in Bannock County, Idaho. We used ArcGIS 10, went through the decision making process, considered several decision criteria, and determined the best location for that store. The process that we developed in this study can also be used in other contexts such as health care, banking, and tourism

Effects of microstructural features, thermal shocks and strain rate on the mechanical response of granitic rocks

Percussive drilling is regarded as the most effective method for excavation, tunneling, and shallow well boring in the hard rock such as granite. However, its efficiency has been questioned in some specific environments and applications such as drilling for geothermal energy, where bores as deep as 5000 m are needed to reach the desired temperature zone. It is therefore understandable that attempts to drill bores that deep can face significant difficulties, and even though these difficulties have already been overcome by developing new techniques for deep drilling, there still are no replacement for the percussive drilling technique. The reason for this situation can be found in the shortage of technological readiness and in the nature of the rock and its behavior itself. However, in the previous attempts to find a replacement for percussive drilling, not enough of attention has been paid to altering the rock’s properties before drilling for example by using a thermal shock.In this work, the mechanical behavior of the rocks before and after applying heat shocks was studied in quasi-static and dynamic loading conditions. Two different heat shocks were applied on the two studied rocks, one using a flame torch and one using a plasma gun. The heat shocks using the flame torch were applied on the Brazilian disc samples with durations of 10, 30, or 60 seconds. The thermal shocks using the plasma gun were applied on the Brazilian disc samples and on the bulk of the rock for dynamic indentation tests. Three different plasma gun heat shocks were applied on Brazilian disc samples with durations of 0.40, 0.55, or 0.80 second. The heat shocks applied on the bulk of the rock had a duration of 3, 4, and 6 seconds.A methodology was developed to analyze and characterize the damage caused by the heat shocks on the surface of the specimens. In this method, a liquid penetrant was applied on the surface of the samples before and after applying the heat shocks with images taken from the specimens’ surface under an ultraviolet light. Later on, the fractal dimension of the surface crack patterns was calculated using the box counting method. The results indicate that the fractal dimension of the samples increases by increasing the duration of the thermal shock and there is a relationship between the relative increase of the fractal dimension and the mechanical response of the rock material. Even though the fractal dimension analysis is limited to the surface of the samples, the computed tomography results suggest that the effects of the heat shocks are also limited to the very surface of the specimens. Therefore, the fractal dimension analysis provides a fast and accurate enough estimation of the mechanical response of the rock.The mechanical behavior of rock was studied at low and high strain rates using the Brazilian disc samples. The results indicate that by increasing the duration of the thermal shock, increasing the fractal dimension, the strength of the rock decreases in the studied strain rate range. Nonetheless, there are some differences in the rock mechanical behavior at low and high strain rates. The dynamic strength of the rock decreases considerably faster with increase of the fractal dimensions than the quasi-static strength. Therefore, the strain rate sensitivity of the rock decreases with the increasing fractal dimension.The dynamic indentation tests were performed to study the effects of heat shocks in situations similar to percussive drilling. The tests were performed using both single and triple button indenters. Even though the direct measurements of the bit-rock interactions obtained from the stress waves are useful, they do not provide any information about the side chipping and chipping between the indenters. Therefore, optical profilometry was used to study the craters formed during the impacts, and the concept of destruction work was used to characterize the effects of the heat shocks on the material removal during dynamic indentation. The results imply that after applying the heat shock, the extent of material removal increases even though the force levels are not affected much. This means that the efficiency of the indentation processes cannot be evaluated only by using the force-displacement curves but additional analysis such as the ones used in this work are needed

High Temperature High Strain Rate Behavior of Superalloy MA 760

The objective of this work was to investigate the high strain rate and high temperature behavior of mechanically alloyed and oxide dispersion strengthened nickel based superalloy MA 760. These types of alloys are used in many high temperature applications, such as turbine blades, where also impact type loadings can occur. Therefore, understanding the behavior of the alloy at its operating temperatures can help designing better and safer components in the cases of high rate impacts and collisions. The high strain rate high temperature tests were carried out using the Split Hopkinson Pressure Bar device at different strain rates and temperatures. The tests were carried out at strain rates between 1050 s-1 and 3800 s-1 and at temperatures ranging from room temperature up to 900 ⁰C. The obtained data was analyzed based on the principles of the Split Hopkinson Pressure Bar, focusing on the yield strength, strain rate, and fracture strain. Based on the test results, the effects of strain rate and temperature on the mechanical behavior of the MA 760 was described. Yield strength increases as a function of temperature until temperatures close to 700⁰C, after which the yield strength decreases. However, even after this decrease the material is still very strong, which makes this material suitable for high temperature applications. The reason for this observed behavior is the anomalous yielding behavior of the γ’ phase. The flow stress increases with increasing temperature until the maximum. At higher temperatures (above 700 ⁰C), the deformation starts in the γ matrix, which causes the reduction in the yield strength of the material. Around 900 ⁰C, the initial cuboidal microstructure changes its morphology, which leads to the further reduction of the strength of the material. During the work of this thesis, a high temperature apparatus for the Taylor impact test was designed and built. The apparatus consists of the sample holder made of Teflon. The sample is placed in the sample holder with a ceramic wool ring. Two thermocouples are attached to each end of the specimen to monitor the temperature of the specimen. A stopper filled with ceramic wool was built to catch the specimen and the projectile. An induction heater was used to heat up the specimen to the test temperature. The impact process was recorded with a high speed camera to measure the speed of the projectile. The device was successfully tested and the results obtained from the tests were comparable with literature and the result obtained from the Split Hopkinson Pressure Bar

Charge density control of quantum dot lattices

The complexity of physical systems in nature is an obstacle for human desire and curiosity to explore new realms of knowledge. As we go further and further, more powerful computers with higher capability both in processing and storing of information are needed. According to Moore's law, the computational power of devices grows exponentially, meanwhile their size decreases at the same rate. This trend is getting saturated and a new jump into a new scale cannot be avoided. Devices manufactured with smaller size exhibit quantum mechanical behaviour. Due to the intrinsic uncertainty which quantum mechanics has, the behaviour of these systems must be controlled with great precision. Deterministic logical computations cannot be done by these devices, since logical operations need to have well-defined sets of input. This is a crucial concern especially if the set of inputs corresponds to the states of quantum mechanical systems. Quantum optimal control theory lets us identify the constraints one has to consider for the sake of the desired manipulation of quantum mechanical systems. The aim of this project is to exploit the controllability of quantum dot cellular automata which are among the candidates for the next generation of transistors as building blocks of logical circuits

Effects of Test Temperature and Low Temperature Thermal Cycling on the Dynamic Tensile Strength of Granitic Rocks

This paper presents an experimental procedure for the characterization of the granitic rocks on a Mars-like environment. To gain a better understanding of the drilling conditions on Mars, the dynamic tensile behavior of the two granitic rocks was studied using the Brazilian disc test and a Split Hopkinson Pressure Bar. The room temperature tests were performed on the specimens, which had gone through thermal cycling between room temperature and − 70 °C for 0, 10, 15, and 20 cycles. In addition, the high strain rate Brazilian disc tests were carried out on the samples without the thermal cyclic loading at test temperatures of − 30 °C, − 50 °C, and − 70 °C. Microscopy results show that the rocks with different microstructures respond differently to cyclic thermal loading. However, decreasing the test temperature leads to an increasing in the tensile strength of both studied rocks, and the softening of the rocks is observed for both rocks as the temperature reaches − 70 °C. This paper presents a quantitative assessment of the effects of the thermal cyclic loading and temperature on the mechanical behavior of studied rocks in the Mars-like environment. The results of this work will bring new insight into the mechanical response of rock material in extreme environments.acceptedVersionPeer reviewe

Effects of microstructural features, thermal shocks and strain rate on the mechanical response of granitic rocks

Percussive drilling is regarded as the most effective method for excavation, tunneling, and shallow well boring in the hard rock such as granite. However, its efficiency has been questioned in some specific environments and applications such as drilling for geothermal energy, where bores as deep as 5000 m are needed to reach the desired temperature zone. It is therefore understandable that attempts to drill bores that deep can face significant difficulties, and even though these difficulties have already been overcome by developing new techniques for deep drilling, there still are no replacement for the percussive drilling technique. The reason for this situation can be found in the shortage of technological readiness and in the nature of the rock and its behavior itself. However, in the previous attempts to find a replacement for percussive drilling, not enough of attention has been paid to altering the rock’s properties before drilling for example by using a thermal shock.In this work, the mechanical behavior of the rocks before and after applying heat shocks was studied in quasi-static and dynamic loading conditions. Two different heat shocks were applied on the two studied rocks, one using a flame torch and one using a plasma gun. The heat shocks using the flame torch were applied on the Brazilian disc samples with durations of 10, 30, or 60 seconds. The thermal shocks using the plasma gun were applied on the Brazilian disc samples and on the bulk of the rock for dynamic indentation tests. Three different plasma gun heat shocks were applied on Brazilian disc samples with durations of 0.40, 0.55, or 0.80 second. The heat shocks applied on the bulk of the rock had a duration of 3, 4, and 6 seconds.A methodology was developed to analyze and characterize the damage caused by the heat shocks on the surface of the specimens. In this method, a liquid penetrant was applied on the surface of the samples before and after applying the heat shocks with images taken from the specimens’ surface under an ultraviolet light. Later on, the fractal dimension of the surface crack patterns was calculated using the box counting method. The results indicate that the fractal dimension of the samples increases by increasing the duration of the thermal shock and there is a relationship between the relative increase of the fractal dimension and the mechanical response of the rock material. Even though the fractal dimension analysis is limited to the surface of the samples, the computed tomography results suggest that the effects of the heat shocks are also limited to the very surface of the specimens. Therefore, the fractal dimension analysis provides a fast and accurate enough estimation of the mechanical response of the rock.The mechanical behavior of rock was studied at low and high strain rates using the Brazilian disc samples. The results indicate that by increasing the duration of the thermal shock, increasing the fractal dimension, the strength of the rock decreases in the studied strain rate range. Nonetheless, there are some differences in the rock mechanical behavior at low and high strain rates. The dynamic strength of the rock decreases considerably faster with increase of the fractal dimensions than the quasi-static strength. Therefore, the strain rate sensitivity of the rock decreases with the increasing fractal dimension.The dynamic indentation tests were performed to study the effects of heat shocks in situations similar to percussive drilling. The tests were performed using both single and triple button indenters. Even though the direct measurements of the bit-rock interactions obtained from the stress waves are useful, they do not provide any information about the side chipping and chipping between the indenters. Therefore, optical profilometry was used to study the craters formed during the impacts, and the concept of destruction work was used to characterize the effects of the heat shocks on the material removal during dynamic indentation. The results imply that after applying the heat shock, the extent of material removal increases even though the force levels are not affected much. This means that the efficiency of the indentation processes cannot be evaluated only by using the force-displacement curves but additional analysis such as the ones used in this work are needed

Optimal control of charge with local gates in quantum-dot lattices

Semiconductor quantum dots are among the leading candidates for next-generation nanoscale devices due to their tunable size, shape, and low energy consumption. Here we apply quantum optimal control theory to coherently manipulate the single-electron charge distribution in quantum-dot lattices of various sizes. In particular, we show that to control the charge distribution it is sufficient to optimize the gate voltage acting on a single quantum dot in the lattice. We generally find yields around 99% in the picosecond time scale when using realistic models for the quantum-dot lattices on a real-space grid. We analyze and discuss both the limitations of the model regarding the gate parameters as well as the potential of the scheme for applications as quantum-dot cellular automata

Sequential quantum cloning under real-life conditions

We consider a sequential implementation of the optimal quantum cloning machine of Gisin and Massar and propose optimization protocols for experimental realization of such a quantum cloner subject to the real-life restrictions. We demonstrate how exploiting the matrix-product state (MPS) formalism and the ensuing variational optimization techniques reveals the intriguing algebraic structure of the Gisin-Massar output of the cloning procedure and brings about significant improvements to the optimality of the sequential cloning prescription of Delgado et al [Phys. Rev. Lett. 98, 150502 (2007)]. Our numerical results show that the orthodox paradigm of optimal quantum cloning can in practice be realized in a much more economical manner by utilizing a considerably lesser amount of informational and numerical resources than hitherto estimated. Instead of the previously predicted linear scaling of the required ancilla dimension D with the number of qubits n, our recipe allows a realization of such a sequential cloning setup with an experimentally manageable ancilla of dimension at most D=3 up to n=15 qubits. We also address satisfactorily the possibility of providing an optimal range of sequential ancilla-qubit interactions for optimal cloning of arbitrary states under realistic experimental circumstances when only a restricted class of such bipartite interactions can be engineered in practice.Comment: 8 pages, 4 figure