The (Coarse) Fine-Grained Structure of NP-Hard SAT and CSP Problems

We study the fine-grained complexity of NP-complete satisfiability (SAT) problems and constraint satisfaction problems (CSPs) in the context of the strong exponential-time hypothesis (SETH) , showing non-trivial lower and upper bounds on the running time. Here, by a non-trivial lower bound for a problem SAT (Γ) (respectively CSP (Γ)) with constraint language Γ, we mean a value c 0 > 1 such that the problem cannot be solved in time O ( c n ) for any c < c 0 unless SETH is false, while a non-trivial upper bound is simply an algorithm for the problem running in time O ( c n ) for some c < 2. Such lower bounds have proven extremely elusive, and except for cases where c 0 =2 effectively no such previous bound was known. We achieve this by employing an algebraic framework, studying constraint languages Γ in terms of their algebraic properties. We uncover a powerful algebraic framework where a mild restriction on the allowed constraints offers a concise algebraic characterization. On the relational side we restrict ourselves to Boolean languages closed under variable negation and partial assignment, called sign-symmetric languages. On the algebraic side this results in a description via partial operations arising from system of identities, with a close connection to operations resulting in tractable CSPs, such as near unanimity operations and edge operations . Using this connection we construct improved algorithms for several interesting classes of sign-symmetric languages, and prove explicit lower bounds under SETH. Thus, we find the first example of an NP-complete SAT problem with a non-trivial algorithm which also admits a non-trivial lower bound under SETH. This suggests a dichotomy conjecture with a close connection to the CSP dichotomy theorem: an NP-complete SAT problem admits an improved algorithm if and only if it admits a non-trivial partial invariant of the above form.

Ways to determine reliability in the operation of ship parts made by banding method

In the development of modern shipbuilding conditions and the repair of ship units, a special role is given to the use of basic structural elements consisting of technological parts. When performing these steps, it is important to analyze the properties of the materials from which the technological components of ship equipment are made. Testing should be close to the operating conditions of ship axles and shafts, namely cyclic loading, aggressive and adhesive environment. Therefore, a special factor is the technological control over the sequence of manufacture, selection of materials, surfacing technology. All these requirements can be analyzed and predicted using computer modulation. Investigations of the properties of the transition layers of the weld and the base metal and their effect on the number of load cycles in the tests are also key. All conditions will be met with the optimal selection of the chemical component Ni - Cr, which provide the required level of doping. The hardness of the materials is ensured by the presence of Mg in the metal. Also important are the heat treatment modes that provide the desired final structure of the material for machining and surfacing. For this part and its elements, the best properties in terms of operation in fine austenitic and pearlitic structures. During the operation of ship shafts and axles, the propagation of puncture loads is performed due to the occurrence of final stresses at low-cycle and multi-cycle loads and subsequent fatigue of the structural lattice. When considering the range of materials used in combined structures is very large and includes most welded steels. According to the combination of materials in one unit, it is advisable to distinguish two main groups of structures: with welded joints of steels of the same structural class, but different alloying, and with welded joints of steels of different structural classes. In this regard, the decision to obtain a balanced bandage connection lies in obtaining a fine-grained structure of the weld metal and the seam area.

Microstructure and mechanical properties of Ti3SiC2 MAX phases sintered by hot pressing

The Ti3SiC2 used in this project has been purchased ready-made. This study aimed to investigate the effect of sintering temperature on samples' microstructure and mechanical properties, including three-point flexural strength, Vickers hardness, and fracture toughness. Therefore, Ti3SiC2 samples were sintered under a vacuum atmosphere at a pressure of 35 MPa for 30 minutes at two temperatures of 1500 °C and 1550 °C by hot pressing. The microstructure obtained from the fracture cross-section of the samples shows that by increasing the sintering temperature to 1550 °C, the microstructure of this sample becomes larger than the sintered sample at 1500 °C. Also, increasing the sintering temperature to 1550 °C causes the decomposition of Ti3SiC2 to TiC, which can be seen in the X-ray diffraction pattern (XRD). In addition, the relative density of the sintered sample at 1550 °C is 98.08% which is higher than that of the sintered sample at 1500 °C with the result of 89%. On the other hand, the three-point flexural strength (227.5 MPa), the Vickers hardness (~9 GPa), and the fracture toughness (8.6 MPa.m1/2) of the sintered sample at 1500 °C are higher due to the fine-grained structure.

Regularities of Structure Formation in 30 mm Rods of Thermoelectric Material during Hot Extrusion

In this study, Ingots of (Bi, Sb)2Te3 thermoelectric material with p-type conductivity have been obtained by hot extrusion. The main regularities of hot extrusion of 30 mm rods have been analyzed with the aid of a mathematical simulation on the basis of the joint use of elastic-plastic body approximations. The phase composition, texture and microstructure of the (Bi, Sb)2Te3 solid solutions have been studied using X-ray diffraction and scanning electron microscopy. The thermoelectric properties have been studied using the Harman method. We show that extrusion through a 30 mm diameter die produces a homogeneous strain. The extruded specimens exhibit a fine-grained structure and a clear axial texture in which the cleavage planes are parallel to the extrusion axis. The quantity of defects in the grains of the (Bi, Sb)2Te3 thermoelectric material decreases with an increase in the extrusion rate. An increase in the extrusion temperature leads to a decrease in the Seebeck coefficient and an increase in the electrical conductivity. The specimens extruded at 450 °C and a 0.5 mm/min extrusion rate have the highest thermoelectric figure of merit (Z = 3.2 × 10−3 K−1).

Choice of a method of carbon wire drawing

At present for wire production various methods of drawing are used. To choose an effective drawing method or their combination, a methodology is needed to estimate existing and new methods of drawing. A methodology of simultaneous estimation of strain-stress state of carbon wire in the area of deformation and force conditions of drawing presented. Based on it an analysis of drawing in monolith dies, roller dies of radial-shear broach, classic two- and multi-roller dies was carried out. A module-combined method of drawing was also considered. Recommended modes of reduction for drawing in monolith dies presented. It was shown that to obtain a wire of 4.0 mm diameter max, the drawing in monolith dies is most effective. For production of wire of larger diameters, roller dies are more advisable. Application of the technology of radial-shear deformation enables to obtain a fine-grained structure in the surface layers of wire. It was shown that application of a module comprising a roller die and a monolith die is most effective. An example of drawing of a round wire from 8.0 mm diameter to 3.0 mm diameter by a route developed with their application considered. Recommendations on application of various methods of drawing for wires of diameter from 0.007 mm to 15.0 mm presented.

Grain Boundary Conductance Mechanisms of Ultra-fine Grained CeO2/BaCeO3 Based Electrolytes Fabricated by a Two-step Sintering Process

Aiming to clarify the grain boundary conductance mechanism of CeO2/BaCeO3 based electrolytes suitable for solid oxide fuel cells (SOFCs), Sm, Bi co-doping CeO2/BaCeO3 (80 wt.% Ce0.8Sm0.1Bi0.1O2-δ - 20 wt.% BaCe0.8Sm0.1Bi0.1O3-δ, BiSDC-BCSBi) electrolytes with ultra-fine grained (110-220 nm) and micron (1-1.8 μm) structures were prepared by the two step sintering and conventional sintering method, respectively. Both electrolytes have pure phases corresponding to CeO2 and BaCeO3 without other purities. In the ultra-fine grained structure, apparent grain boundary conductivities measured at 350 oC and 400 oC are 1-2 orders of magnitude higher than micron structures, thus resulting in dramatically enhanced electrical performances. This grain boundary effect can be attributed to two aspects. One is the decrease of space charge potential Δφ(0) (0.165 V for ultrafine-fine grained ones, 0.396 V for micron ones). The other is the dilution of impurities (the impurity blocking term ω/dg is 0.94 for ultrafine-fine grained ones, and 0.53 for micron ones). In the ultra-fine grained electrolytes, no extra electronic conduction is introduced, and the ion migration number of O2- is higher than that of H+. Finally, the ultra-fine grained BiSDC-BCSBi electrolytes maintain a good long-term stability in the operating condition of SOFCs at 600 oC for 100 h.

Effect of ion nitriding by glow discharge on the physical and mechanical properties of the plastically deformed tool steel R6M5

This work is devoted to the study of the effect of the duration of ion nitriding by glow discharge on the physical and mechanical properties of tool steel with different initial structure. We used specimens of R6M5 tool steel with a coarse-grained structure obtained after annealing at a temperature of 850°C and with a fine-grained structure obtained after severe plastic deformation by torsion discharge. With an increase in the duration of ion nitriding, the thickness of the hardened layer and wear resistance increase. The combination of plastic deformation with ion nitriding by glow discharge increases the adsorption and diffusion rate of the saturating element due to the creation of a highly fragmented and disoriented fine-grained structure and contributed to reduction in processing time.

Very High Cycle Fatigue Investigations on the Fatigue Strength of Additive Manufactured and Conventionally Wrought Inconel 718 at 873 K

The fatigue lives of additively manufactured (AM) Inconel 718 (IN718) produced by selective electron beam melting and conventional wrought material as reference conditions were studied in the very high cycle fatigue regime under fully reversed loading (R = −1) at the elevated temperature of 873 K using an ultrasonic fatigue testing system. The fatigue lives of the AM material were significantly reduced compared to the wrought material, which is discussed in relation to the microstructure and a fractographical analysis. The additively manufactured material showed large columnar grains with a favoured orientation to the building direction and porosity, whereas the wrought material showed a fine-grained structure with no significant texture, but had Nb- and Ti-rich non-metallic inclusions. Crystallographic crack initiation as well as crack initiation from the surface or internal defects were observed for the AM and the wrought IN718, respectively.

A fine-grained analysis of a Monk parakeet (Myiopsitta monachus) nest suggests a nonhomogeneous internal structure

We report first data on the fine-grained structure (branch diameter, length and diversity) in three different sectors [core (central side), buffer (peripheral side), and nest chamber)] of a nest of Monk Parakeets (Myiopsitta monachus) from a non-native breeding site located in an urban park (Rome, central Italy). The central core sector was characterized by longer and thicker branches capable of supporting the nest. The peripheral part (buffer) was characterized by less long and less thick branches with the function of completing the structure. Branches building the nest chamber were shorter and less thick but very diversified in size, because they included both small branches supplied inside the chamber and longer branches covering it. This diversification of the internal chamber (nest chamber) could be functional to maintain stable temperatures of incubator chambers compared to large fluctuations outside the nest. The presence of leaves of herbaceous species (Hordeum leporinum) could play a bactericidal role for the nest plant material.

Using FCAW with Electrodes Based on Fe-Ti-Mo-B-C System for Increasing of Durability of Junk Removal Tools

In this work were analyzed factors and working conditions that leads to the wearing of junk mills tools that are a part of junk removal equipment used in drilling and workover of borehole. Such equipment is a part of oil and gas industry and work under condition of intense abrasive wearing with increased pressures and cyclic loads. Was established that traditional hardfacing materials based on the Fe-Cr-C system are not effective for improvement of abrasion resistance of elements of such equipment due to their low crack resistance and low hardness of chromium carbides. The aim of this work was to increase a durability of that equipment by using of flux cored electrodes with reaction components of pure metal powders, which leads to forming the fine-grained structure with increased hardness. Powders of Ti, Mo, B4C and their combinations were used. Structures of the hardfacing coatings were investigated by method of metallography, scanning electron microscopy (SEM). Abrasion wear tests were held under condition of fixed and non-fixed abrasion. Using of pure metal powders led to formation of a fine-grained structure with grains of Mo2FeB2 that forms around TiC, which work as modifier. It was investigated that the researched material based on Fe-Ti-Mo-C-B system that was used for increasing the wear resistance of junk mills led to increasing of the TBO period in 1.5-1.6 times comparing with serial hardfacing materials based on tungsten.