Typical Square Research Articles

Average-case analysis of the Gaussian elimination with partial pivoting

The Gaussian elimination with partial pivoting (GEPP) is a classical algorithm for solving systems of linear equations. Although in specific cases the loss of precision in GEPP due to roundoff errors can be very significant, empirical evidence strongly suggests that for a typical square coefficient matrix, GEPP is numerically stable. We obtain a (partial) theoretical justification of this phenomenon by showing that, given the random n×n\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$n\ imes n$$\\end{document} standard Gaussian coefficient matrix A, the growth factor of the Gaussian elimination with partial pivoting is at most polynomially large in n with probability close to one. This implies that with probability close to one the number of bits of precision sufficient to solve Ax=b\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$Ax = b$$\\end{document} to m bits of accuracy using GEPP is m+O(logn)\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$m+O(\\log n)$$\\end{document}, which improves an earlier estimate m+O(log2n)\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$m+O(\\log ^2 n)$$\\end{document} of Sankar, and which we conjecture to be optimal by the order of magnitude. We further provide tail estimates of the growth factor which can be used to support the empirical observation that GEPP is more stable than the Gaussian Elimination with no pivoting.

Assessment on natural ventilation and pollutant dispersion around sunken squares by transient simulation

Sunken square is a semi-open public space that has been gaining popularity in urban planning and designs. Its semi-open design is beneficial to ventilation of the connected underground spaces, but it is also subject to potential exposure to ground-level traffic pollutants. To evaluate the semi-open design’s influence on the balance between underground ventilation efficiency and the pollutant exposure, this study uses large eddy simulation (LES) to simulate turbulent wind flow characteristics and pollutant dispersion in a typical sunken square. The sunken square is connected to two indoor spaces with single-sided opening, and the design features of staircase and arcade are further tested for their influences on the wind flow field. The air change rate per hour (ACH, h−1) is adopted to quantify the ventilation efficiency of the two connected indoor spaces. Results show that the staircases amplify wind velocities for the indoor spaces but also bring higher pollutant concentrations inside together. Moreover, the design of the arcade at the opening prompts the vortex to shift towards the entrance, leading to a heightened concentration of pollutants. Meanwhile, the effective ACH is mostly contributed by the turbulent diffusion (ACHt), while the mean flow (ACHm) has much less effect on the ventilation of the indoor spaces. These findings of this study provide references for sunken square design.

Rayleigh analysis and numerical simulations of metal-mesh/ transparent conducting oxide composite transparent electrode

Transparent conducting oxides (TCOs), especially indium tin oxides (ITOs), have played an important role in realizing optoelectronics devices. Composite electrodes fabricated by introducing different types of metal-meshes into TCO have exhibited improved electric properties as well as good transparency. This technology can also reduce the demand for ITO and provide the candidates of flexible electrodes for wearable devices. Analysis of the electric properties of this type of electrode, such as the variance of the sheet resistance of the composite electrodes with the embedded mesh structure parameters, can provide a theoretical basis for designing and fabricating this electrode. But detailed studies are still lacking. This work focuses on the electrical property analysis of the typical square hole and grid shaped metal mesh-TCO composite electrodes based on Rayleigh model and finite-element simulation, respectively. The electric potential distribution and current density distribution are obtained from the finite element calculations, revealing that the dramatic deformation of the metallic channels in the composite results in the failure of a conventional Rayleigh model for the moderate and high opening rates. Accordingly, we adopt a lattice correction to the Rayleigh model to reduce the channel deformation by increasing the symmetry of the exterior boundary of the lattice cell. A comparison of the results from the simulations with those from the second-order approximation of the lattice-adapted Rayleigh model shows that the new analytic form of the effective conductivity is applicable to a much larger opening-rate range for both the monolayer and the sandwich structures of metal-mesh TCO composite electrodes. The variances of the sheet resistance and the effective conductivity with different material and structure parameters of the composite electrodes are calculated and discussed based on the lattice-adapted Rayleigh approximation. The results are well consistent with experimental results. A comparison of our model with other theoretical models is also made, showing that this lattice-adapted Rayleigh approximation can be used as a simple and efficient theoretical tool to analyze and design the concerned transparent composite electrodes.

Grain shape-protrusion-based modeling and analysis of material removal in robotic belt grinding

The accurate prediction of material removal (MR) remains a persistent challenge in the field of robotic belt grinding, particularly with the consideration of the stochastic nature of abrasive grains. Starting from the characteristics that abrasive grains with different shapes participate in grinding, this work presents a novel MR model that extends from microscopic grain-workpiece interaction to macroscopic wheel-curved surface contact. Specifically, the irregular shapes of single abrasive grains are generalized into four typical types, namely, semi-sphere, cone, equilateral-triangular pyramid, and square pyramid. Based on the effective abrasive grains determined by stochastic grain protrusion heights, the microscopic contact force and material removal volume shared by different effective individual abrasive grains are modeled and analyzed subsequently. Together with the macroscopic contact pressure solved by the Hertzian contact theory, the material removal model is derived by considering the geometrical characteristics of different-shaped abrasive grains. Finally, the grinding experiments on the Ti–6Al–4V test block and aero-engine blade were conducted under controllable grinding parameters, through which the effectiveness and applicability of the proposed model were validated, and the material removal characteristics with different structured abrasive belts were investigated.

Energy absorption and topology optimization of self-similar inspired multi-cell square tubes

Due to their low cost and lightweight properties, multi-cell square tubes have been widely used in impact protection as energy absorbers. In this study, two kinds of multi-cell square tubes were constructed according to the local self-similar and global self-similar layout strategies. The experiments and numerical simulations were conducted to investigate their quasi-static compression deformation and energy absorption. The results demonstrated that self-similar layout strategies can significantly enhance the crashworthiness of multi-cell square tubes, and the global self-similar layout appears to be more effective at energy absorption. A simplified theoretical model for the mean crushing force (MCF) was developed for its constituent elements of the proposed square tubes. Furthermore, the COPRAS method and the non-dominated sorting genetic algorithm II (NSGA-II) were employed for optimal structure selection and multi-objective optimization. The results showed that the 2nd-order global self-similar multi-cell square tube (MSTG1-2) had prominent crashworthiness compared with some typical self-similar square tubes. The current optimization and topology design strategies can be used in other polygonal multi-cell tubes, which provides an effective guide for enhancing the crashworthiness of these multi-cell tubes.

A phase unwrapping method with the sparse prior for diffraction phase microscopy

Phase unwrapping is widely used in interferometry. In the typical least square (LS) method, the noise in the wrapped phase cannot be removed. An improved algorithm based on total variation (TV) imposes L1-norm on the image gradient to improve the sparsity. However, it may lead to over-sparsity, and the unwrapped phase will be compressed if the penalty term is overlarge. In this study, we proposed a sparse prior phase unwrapping (SPUP) algorithm to solve the wrapped phase of interferograms of diffraction phase microscopy (DPM). Since DPM has a unique sample sparsity in the imaging field of high-power objectives, the L0-norm and L1-norm regularizations are introduced into the SPUP process. The results verify the strong denoising ability and high phase fidelity of the proposed SPUP method. Moreover, the uneven background noise and phase shifting of DPM interferograms could be corrected, demonstrating the great potential of the SPUP method in various interferometry measurements.

Penta-MN8 family: First realization of type-5 pentagonal tessellation in 2D hexagonal crystals with intriguing properties

Tessellation of the Euclidean plane by congruent pentagons has long been of great interest. However, periodic pentagonal patterns realized in crystallography reported so far are limited to type-2 or type-4 tiling in typical square lattices. Based on the recently synthesized N18 macrocycles together with Hückel aromaticity and 18-electron rules, we design a family of pentagonal metal polynitrides, penta-MN8 (M = Mg, Ca, Sr, Ba; Sn, Pb; Cd; Mo, W), the first materials realization of type-5 mathematical pattern with novel pentagonal tiles in 2D hexagonal lattices. The penta-MN8 family exhibits rich stable phases (γ, α/α′, and β) and diverse Poisson's ratios ranging from 0.299 to -0.488. Among these nitrogen-richest monolayer nitrides hitherto, penta-MgN8 possesses firm stability up to 700 K and under low pressure originating from unique aromaticity over the polymeric nitrogen network, which could be synthesized under ∼50 GPa as confirmed by global structure search. Moreover, penta-MgN8 exhibits a fully flat band near Fermi level over the whole 2D Brillouin zone, deriving from the combination of pentagonal pattern and hexagonal lattice as verified with tight-binding model analysis. Such electronic structures fill in the blank of clear kagome flat bands in known kagome nitrides and pentagon-based materials, resulting in very heavy fermions with huge effective mass (55.7 m0) that are favorable to achieve quantum zero-field Wigner crystals. Our work presents a new pentagonal-materials class with unprecedented coordination, lattice symmetry, and physical properties compared to existing pentagon-based systems, which makes a breakthrough in exploring the materials realization of the mathematical models for pentagonal tessellation.

Prefabricated Ferrocement Jacket for Repairing and Strengthening Axially Loaded Square Sub-Standard Concrete Stub Columns

For decades, ferrocement has been used to repair, strengthen, and even build structural components because it is a long-lasting and reasonably priced material. However, onsite ferrocement jacketing is time-consuming and labour-intensive. Alternatively, prefabricated ferrocement jacket installation eliminates these shortcomings. Therefore, this study utilises wearable prefabricated ferrocement jackets to repair and strengthen axially loaded sub-standard low-strength concrete elements. In order to repair cracked specimens and strengthen existing intact specimens, two types of wearable prefabricated jackets are proposed, ‘L’ shape and ‘U’ shape. Besides a control specimen, two preloaded and two unloaded square concrete specimens were utilised to repair and strengthen using the Prefabricated Ferrocement Jacketing system. The test results and crack patterns show that all the jacketed specimens performed better than the control specimens in terms of load-bearing capacity, ultimate axial and lateral deflection, and ductility. In terms of load-bearing capacity, the unloaded strengthened specimens showed significant results consistently. Based on the results, the proposed solutions were found to be effective in solving the problem of typical square ferrocement jackets.

The Effect of Green Roofs and Green Façades in the Pedestrian Thermal Comfort of a Mediterranean Urban Residential Area

The present study investigated the cooling effect of extensive green roofs and green façades, at the pedestrian level, of a Mediterranean densely populated neighborhood. The ENVI-met environmental model was employed to simulate the microclimatic environment on a typical summer day. Thermal conditions of the study area were evaluated based on air temperature and the Mediterranean thermal stress scale of UTCI (Universal Thermal Climate Index). Three mitigation strategies were developed to ameliorate the thermal conditions in the examined area focusing on the efficacy of green façades, green roofs, and the synergetic effect of the green façade and green roof. The mitigation strategies’ performance was evaluated in characteristic design layouts of the study area, namely the following: a typical Mediterranean square, a church with a churchyard, an avenue, NS and EW street orientations, and courtyards. Results showed that compared to the existing configuration, the synergetic effect of the green façade and green roof achieved the greatest amelioration of the thermal conditions during the hottest hours of the day (12:00–18:00) since it produced an average Tair reduction of up to 0.7 °C and a UTCI reduction of 1.6 °C (both in the courtyards design layout). Among the examined design layouts, the courtyards produced the greatest reductions in air temperature and UTCI, whereas the EW streets were the lowest.

(433) Eros and (25143) Itokawa surface properties from reflectance spectra

Context. Our knowledge of near-Earth asteroid (NEA) composition is important for planetary research, planetary defence, and future in-space resource utilisation. Upcoming space missions, for example, Hera, M-ARGO, or missions to the asteroid (99942) Apophis, will provide us with surface-resolved NEA reflectance spectra. Neural networks are useful tools for analysing reflectance spectra and determining material composition with high precision and low processing time. Aims. We applied neural-network models on disk-resolved spectra of the Eros and Itokawa asteroids observed by the NEAR Shoemaker and Hayabusa spacecraft. With this approach, the mineral variations or intensity of space weathering can be mapped. Methods. We built and tested two types of convolutional neural networks (CNNs). The first one was trained using asteroid reflectance spectra with known taxonomy classes. The other one used silicate reflectance spectra with assigned mineral abundances and compositions. Results. The reliability of the classification model depends on the resolution of reflectance spectra. Typical F1 score and Cohen's κC values decrease from about 0.90 for high-resolution spectra to about 0.70 for low-resolution spectra. The predicted silicate composition does not strongly depend on spectrum resolution and coverage of the 2-µm band of pyroxene. The typical root mean square error is between 6 and 10 percentage points. For the Eros and Itokawa asteroids, the predicted taxonomy classes favour the S-type and the predicted surface compositions are homogeneous and correspond to the composition of L/LL and LL ordinary chondrites, respectively. On the Itokawa surface, the model identified fresh spots that were connected with craters or coarse-grain areas. Conclusions. The neural network models trained with measured spectra of asteroids and silicate samples are suitable for deriving surface silicate mineralogy with a reasonable level of accuracy. The predicted surface mineralogy is comparable to the mineralogy of returned samples measured in the laboratory. Moreover, the taxonomical predictions can point out locations of fresher areas.

Pd(II)dipyrrinato complexes: Synthesis, crystal structure and their antibacterial applications

The synthesis and biological studies of a series of Pd(II)dipyrrinato complexes are reported. The thiogalactosyl and/or oligoethyleneglycol moieties were linked with themeso-aryl rings of the Pd(II)dipyrrinato complexes. The Pd(II)dipyrrinato complexes were characterized by MASS, IR, UV-Vis, and NMR spectroscopic techniques. Single crystal X-ray structure of the homoleptic Pd(II)dipyrrinato complex (Pd1) revealed typical square planar geometry around the metal center. The anti-bacterial studies of Pd(II) dipyrrinato complexes were performed on theM. Tuberculosis H37Rv and M. Bovis BCG strains and complex Pd4 showed excellent anti-TB activity with MIC values of 25 [Formula: see text]M and 12.5 [Formula: see text]M, respectively. The ease of synthesis and good MIC values of Pd(II)dipyrrinato complexes make them promising candidates for anti-TB activity.

Non-equivalent nature of acetylenic bonds in typical square graphynes and intricate negative differential resistance characteristics

The role of acetylenic linkage in determining the exotic band structures of 4, 12, 2- and 4, 12, 4- graphynes is reported. The Dirac bands, as confirmed by both density functional theory and tight-binding calculations, are robust and stable over a wide range of hopping parameters between -hybridized carbon atoms. The shifting of the crossing points of the Dirac bands along the k-path of these two square graphynes is found to be in opposite direction with the hopping along with the acetylenic bond. A real space decimation scheme has also been adopted for understanding this interesting behavior of the band structure of these two graphynes. The condition for the appearance of a nodal ring in the band structure has been explored and critically tested by appropriate Boron-Nitrogen doping. Moreover, both the graphynes exhibit negative differential resistance in their current–voltage characteristics, with 4, 12, 2- graphynes showing superiority.

Gold Teflates Revisited: From the Lewis Superacid [Au(OTeF5 )3 ] to the Anion [Au(OTeF5 )4

A new synthetic access to the Lewis acid [Au(OTeF5 )3 ] and the preparation of the related, unprecedented anion [Au(OTeF5 )4 ]- with inorganic or organic cations starting from commercially available and easy-to-handle gold chlorides are presented. In this first extensive study of the Lewis acidity of a transition-metal teflate complex by using different experimental and quantum chemical methods, [Au(OTeF5 )3 ] was classified as a Lewis superacid. The solid-state structure of the triphenylphosphine oxide adduct [Au(OPPh3 )(OTeF5 )3 ] was determined, representing the first structural characterization of an adduct of this highly reactive [Au(OTeF5 )3 ]. Therein, the coordination environment around the gold center slightly deviates from the typical square planar geometry. The [Au(OTeF5 )4 ]- anion shows a similar coordination motif.

An Online Condition-Based Parameter Identification Switching Algorithm for Lithium-Ion Batteries in Electric Vehicles

Safely and reliably managing the lithium-ion batteries in electric vehicles for daily operations relies on accurate state-of-charge estimation. To pursue accurate state-of-charge estimation, battery electric circuit model-based algorithms demand minimized modeling error from accurate parameter identifications. Typical online parameter identification algorithms: least square fitting approach and recursive least square fitting are commonly adopted but have their limitations and issues with continuously providing accurate identification results. To overcome their problems and utilize their strengths, this paper proposes a condition-based parameter identification switching algorithm. The proposed algorithm accurately and robustly identifies the lithium-ion batteries' parameters based on the battery data condition and the adoption of Bollinger bands. By minimizing the modeling error, the accuracy of the state-of-charge estimation is thus improved. The electric vehicle simulation results indicate that the proposed algorithm can improve the parameter identification accuracy by an average of 70.80% and 44.95% reduction in the mean absolute parameter identification error, compared to typical least square fitting and recursive least square fitting approaches. With the help of the minimized modeling error, the state-of-charge estimation accuracy can thus be improved, rendering an average of 62.44% and 21.49% improvement.

Enhanced Signal Detection and Constellation Design for Massive SIMO Communications With 1-Bit ADCs

In this paper, we investigate a transmitter and receiver design for a single-user massive SIMO (single-input multiple-output) system with 1-bit analog-to-digital converters (ADCs) at the base station (BS), where the user adopts higher-order modulation, e.g., 16-quadrature amplitude modulation (16-QAM), for the data transmission. For the channel estimation and the signal detection, linear least-squares (LS) estimation and maximum ratio combining (MRC) are respectively employed. In this context, we first introduce closed-form formulas for the mean of the estimated symbols and for the correlation matrix between their real and imaginary parts considering the effect of 1-bit quantization. The study of the distribution of the estimated symbols indicates that, in presence of 1-bit ADCs, the conventional 16-QAM detector and the typical square 16-QAM modulation are not adequate. In light of this, we propose three novel symbol detectors and re-design the 16-QAM modulation in order to improve the symbol error rate (SER). Furthermore, the upper bound on the SER is analyzed based on the pair-wise error probability and the boundary equation between two regions is also studied. Through numerical results, the proposed framework, i.e., the symbol detector and the transmit constellation design, shows a significant enhancement in the SER performance against the conventional detector and the typical square 16-QAM modulation.

Numerical investigation into heat transfer augmentation in a square minichannel heat sink using butterfly inserts

Heat transfer augmentation in a square minichannel heat sink through introduction of various butterfly insert configurations is numerically investigated for a range of Reynolds numbers (200 – 900). The present study also examines the individual effects of insert, pitch of the insert, and perforations in the wings of the butterfly insert on the thermohydraulic performance of minichannel heat sinks. Incorporating any kind of insert in a typical square minichannel is found to have a positive influence on the overall thermohydraulic performance, yielding performance evaluation criteria consistently over unity for the whole range of tested Reynolds numbers. The effect of pitch is tested for unperforated inserts, wherein a reduction of pitch distance from 10 mm to 5 mm is found to increase heat transfer performance by 15.08 - 46.39% for the studied range of Reynolds numbers. Perforations in the wings of butterfly inserts are found to result in a reduction of friction factor, with a 4.01 – 20.78% decrease, when compared with an unperforated insert having an identical pitch. However, this reduction is achieved at the cost of a lower heat transfer performance (5.07 – 16.17%). Therefore, unperforated butterfly inserts are deemed to be superior in terms of the overall thermohydraulic enhancement. In all enhanced minichannel configurations, a redistribution of velocity and temperature fields due to the formation of a primary vortex pair and thinning of thermal boundary layers due to a second pair of secondary vortices are thought to be the major contributors behind the observed thermohydraulic enhancement. • Introduction of a butterfly insert with 10 mm pitch is found to enhance heat transfer performance in MCHS by 42.02% to 109.31% for the tested range of Reynolds numbers. • A reduction in pitch from 10 mm to 5 mm in an MCHS with unperforated butterfly inserts is observed to yield an augmentation of average Nusselt number by 15.08% to 46.39% for the studied range of Reynolds numbers. • Perforation on insert wings is found produce a reduced enhancement in average Nusselt number, i.e., 5.07%–16.17%, for the investigated range of Reynolds numbers. • Observed thinning and disruption of thermal boundary layers and enhanced fluid mixing at the central region of the minichannel due to a pair of primary vortices are thought to be the major reasons for enhanced thermal performance. • A maximum performance evaluation criterion of 1.66 is observed for the case of unperforated butterfly inserts with 5 mm pitch at a Reynolds number of 900.

Phenanthrodiazaporphyrins: 1,10-Phenanthroline-Embedded Diazaporphyrin Analogues

Abstract A series of metal-free and metallo-diazaporphyrin analogues embedded with a 1,10-phenanthroline unit were synthesized and characterized. The molecular structure of the Ni(II) complex determined by single-crystal X-ray diffraction analysis confirmed its monocationic character in which the metal center adopts a typical square planar geometry binding with the pyrrole and phenanthroline nitrogen atoms. The spectroscopic and electrochemical studies, as well as molecular orbital calculations suggested that the metal complexes can be classified as 4nπ non-aromatic compounds.

Improvement Strategies for Microclimate and Thermal Comfort for Urban Squares: A Case of a Cold Climate Area in China

Urban squares are an important part of a city’s overall spatial environment. However, many urban squares lack rational designs, causing the thermal environment to deteriorate. To ensure sustainable urban development, urban square microclimates should be improved. Given that, this study investigates the effects of three coverages of three landscape elements of urban squares through modeling and simulation using the ENVI-met model validated by field measurements. The correlation between physiological equivalent temperature (PET) and different amounts of landscape elements is investigated using Spearman analysis. This study presents a case study of a typical urban square in a cold climate area. Design strategies in the area are proposed. The results show that the microclimate and thermal comfort of the urban square can be improved by expanding water bodies, modest increasing buildings and optimizing vegetation. Vegetation is the most important landscape element affecting thermal comfort in the urban square. The PET can be reduced by about 1.5 °C by increasing the vegetation cover from 40% to 70%. However, the degree of microclimate regulation by vegetation is disturbed by water bodies and buildings (|ρ| ≥ 0.5). Therefore, to achieve a more comfortable thermal environment, a combination of landscape elements should be considered.

Ultrasimple and Ultrafast Method of Optical Modulation by Perovskite Quantum Dot Attachment to a Graphene Surface

Optical modulation is the process of modifying the structure and elemental composition of materials so that the main optical parameters, including amplitude, frequency, and phase, are changed. Currently, much research attention has been directed toward ultrafast dynamics, but the process of modulation is often complex. To simplify the optical modulation process and improve the optical properties of perovskites for semiconductor quantum dot (QD) lasers, the process and physical mechanism underlying graphene QD ultrafast modulation of the optical properties of perovskite CsPbBr3 QDs were investigated. The typical cubic structure and square shape of CsPbBr3 QDs were characterized by transmission electron microscopy and X-ray diffraction, respectively. A luminescent peak centered near 540 nm and Stokes shift of 21.34 nm of CsPbBr3 QDs without graphene QDs were measured by absorption and photoluminescence spectroscopy. A maximum modulation shift of 133 nm and a modulation depth of 900% were achieved in CsPbBr3 with graphene. The results indicated that graphene QDs had the best modulation effect on perovskites when the drop volume was 0.05 mL. The process of ultrafast optical modulation via graphene QDs occurring within 1 ps was confirmed by the transient absorption spectrum. The modulation mechanism of graphene to perovskites is presented for guidance. This paper can be used as a reference for the optical modulation of perovskite materials.

Research on the Spatio-Temporal Differentiation Characteristics and Factors of Typical Square Cities in China from the Perspective of Human Settlements

Taking Dalian, a typical square city in China, as an example based on data from remote sensing images, questionnaires, spatial statistics, social economy, etc., 48 squares in the main districts were constructed from the perspective of human settlements in order to build five systems: nature, humanity, society, residence and support. The aim was to explore the spatio-temporal differentiation characteristics and their driving mechanism. The results show the following: (1) The index system was constructed based on the human settlements perspective, and PCA was used to comprehensively evaluate it. Four principal component factors were extracted, and their cumulative contribution rate is 78.701%. On this basis, city squares were divided into four types: comprehensive square, recreational square, commercial service square and traffic square. (2) Using Mapinfo to visualize the square space, and taking the People’s Square as the center, the squares from the Tsarist Russia and Japanese colonial rule time periods were mainly distributed within 5 km, mostly in the direction of NE-SEE. During the construction of New China, city squares were distributed in all directions of the city, mainly between NE-SE and NNW-SSW. (3) ArcGIS was used to create an analysis chart of square service scope. Compared with 1999, it was more concentrated in central cities in 2016, and the service scope was relatively small. However, a square with high popularity has a wider influence. (4) The formation and evolution of the spatial pattern of city squares are affected by many factors, such as nature, economy, society, politics, ecological environment and technology. In the planning and development of city squares, Dalian should pay full attention to human settlements perpectives and add luster to the development of livable cities.