Interior Conditions Research Articles

Evaluating the Effective Factors of Hospital Rooms on Patients' Recovery Using the Data Mining Method.

This study aims to investigate the effective environmental factors of hospital rooms in patients' recovery through data mining techniques. Previous studies have shown the positive effect of the interior environment of the hospitals on patients' recovery. The methods of these studies were mainly based on the evidence and patients' perception while hospital environments are associated with a large amount of data that make them an appropriate case for data mining studies. But data mining studies in hospitals mainly focused on medical and management purposes rather than evaluating the interior environment condition. We analyzed the hospital information system data of a hospital using Python programming language and some of its libraries. Preprocessing and eliminating the outliers, labeling and clustering of diseases, data visualization and analysis, final evaluation, and concluding were done using the knowledge discovery in databases process. Pearson coefficient value for rooms' area was .5 and, respectively, for the distance from the ward entrance and nursing station were .75 and .70. The χ2 values for the variables of room types, location, and occupation were 24.62, 18.98, and 21.53, respectively, and for the beds' location was 0.12. The results confirmed the correlation of the length of stay with the room types, location, and occupation, distance from the nursing station and ward entrance and also showed a moderate correlation with the rooms' area. However, no evidence was found about the relationship between the beds' location in rooms and patients' length of hospital stay.

Exploring the biotic homogenization and diversity resistance hypotheses: The understorey of non‐native and native woodland canopies in three urban areas of Europe

AbstractAimExploring the biotic homogenization and diversity resistance hypotheses by assessing the effect of non‐native black locust canopy on understorey species turnover.LocationBerlin, the Venetian metropolitan area, and Rome.MethodsWe modelled the zeta (ζ) expression of diversity to compare the understorey species turnover between the non‐native black locust and native woodland canopies across multiple sites and through predictors of anthropogenic pressure (road and built‐up density) and interior conditions (tree basal area and mean height).ResultsIn Rome, black locust showed the lowest survivability and cover and did not produce any homogenization of the understorey. In Berlin and in the Venetian metropolitan area, black locust caused understorey homogenization, although with a lower intensity in Berlin. Under black locust canopies, distance between sites and road density was more consistently associated with species turnover, across urban areas and multiple sites. Under native canopies in Berlin, factors prominently associated with species turnover were road and built‐up density and mean tree height, while in the Venetian metropolitan area it was road density.Main conclusionsEvidence in support of the biotic homogenization in contrast to the diversity resistance hypothesis varied across urban areas. Species turnover was influenced by land use patterns more evidently under native tree canopies and where the non‐native tree had higher survivability. Similar analyses in other urban areas may confirm these relationships with other types of landscapes.

Digital simulation trial of hydroisostasy by finite element method

Hydroisostasy as a geodynamic phenomenon was discovered along investigation sea level changes of the World
 Ocean as result of intakes water to glaciers during Glacial period and releasing back during Interglacials. The water loads
 under sea level changes influenced the change of solid Earth shape and make the contribution to the vertical Earth crust
 movement along shorelines areas. A vertical shorelines movements are critical issue of the longtime living infrastructure coast
 facilities design with the overflooding and overdrainage forecast.
 The main method of hydroisostasy phenomenon investigation is remain the digital simulation. The global character of phenomenon
 require simulation involving all planet volume and detail accounting of the lithosphere and mantle layers features
 for each region which is forced to use 3-D modeling with high resolution and require big computing resources.
 Finite element method with ability to assign boundary conditions allow to use local-regions models with enough resolutions
 and take into accounts local lithosphere and mantle features without involving big computing resources.
 One of the free software packs with open code and possibility applying FEM for geodynamics simulations is — ELMER, software
 designed and supported by Finland CSC — IT CENTER FOR SCIENCE LTD.
 The trial applying of ELMER software packs for modeling hydroisostasy phenomenon for Earth interior conditions close to
 Deryugin depression in Okhotsk sea in this study has done. A plausible and encouraging result obtained for continuation of
 research in more detail.

Measuring the structure and equation of state of polyethylene terephthalate at megabar pressures

We present structure and equation of state (EOS) measurements of biaxially orientated polyethylene terephthalate (PET, ({hbox {C}}_{10} {hbox {H}}_8 {hbox {O}}_4)_n, also called mylar) shock-compressed to (155 pm 20) GPa and (6000 pm 1000) K using in situ X-ray diffraction, Doppler velocimetry, and optical pyrometry. Comparing to density functional theory molecular dynamics (DFT-MD) simulations, we find a highly correlated liquid at conditions differing from predictions by some equations of state tables, which underlines the influence of complex chemical interactions in this regime. EOS calculations from ab initio DFT-MD simulations and shock Hugoniot measurements of density, pressure and temperature confirm the discrepancy to these tables and present an experimentally benchmarked correction to the description of PET as an exemplary material to represent the mixture of light elements at planetary interior conditions.

An adaptive thermal comfort model for naturally ventilated classrooms of technical institutions in Madurai

PurposeOccupants dwelling in hot climatic regions of India for a longer term are tolerable to high temperature levels than predicted by American Society of Heating, Refrigerating and Air-Conditioning Engineers (ASHRAE) standards. The purpose of this study is to evaluate the thermal sensations (TS) and neutral temperature of the occupants in naturally ventilated (NV) and air-conditioned (AC) classrooms of two technical institutions located in the same premises in the suburbs of Madurai. The main focus of this study is to understand the occupants’ behaviour in response to the thermal conditions of the educational buildings particularly in the warm and humid climatic zone of Madurai.Design/methodology/approachThis research collected data through field studies. The data included 383 survey questionnaires from NV classrooms and 285 from AC classrooms, as well as on-site measurements of interior and exterior weather conditions. The TS results show that the students preferred well-designed NV classrooms than AC classrooms. A new adaptive comfort equation derived from this study can be applied to NV classrooms in warm and humid climates where mean outdoor temperature exceeds 40°C.FindingsThe neutral temperature derived for NV classrooms in Madurai ranged from 29°C to 34°C. Thus, the occupants in the NV classrooms of the higher learning educational institutions in the warm and humid climatic region of Madurai can adapt well to higher indoor temperature levels than predicted by ASHRAE comfort levels with minimum adjustments.Research limitations/implicationsThe study was limited to only occupants in two premier higher learning technical educational institutions located in Madurai region within 5–10 km within the city limits to understand the implications of microclimate with respect to the urban context. Thus, further research is required to examine the tendency under local conditions in other regions beyond those applied to this study.Social implicationsThe findings of this study showed that occupants in higher learning educational intuitions in Madurai prefer NV classrooms than AC classrooms. Therefore, with rising demands of energy use for mechanical ventilation and the associated high cost for running AC buildings, architects should prioritize the design of energy efficient buildings through the optimal use of passive design strategies for ventilation and thermal comfort. This study gives a base data for architects to understand the adaptive limitations of occupants and design NV buildings that can promote natural ventilation and provide better thermal environments that can help increase the productivity of students.Originality/valueThis paper was an attempt to develop the adaptive comfort model for NV classrooms in Madurai regions. There has been no attempt to identify the adaptive comfort levels of occupants in higher learning technical educational institutions located in warm and humid climatic region of India.

Internal resistive heating of non-metallic samples to 3000K and >60GPa in the diamond anvil cell.

High pressure-temperature experiments provide information on the phase diagrams and physical characteristics of matter at extreme conditions and offer a synthesis pathway for novel materials with useful properties. Experiments recreating the conditions of planetary interiors provide important constraints on the physical properties of constituent phases and are key to developing models of planetary processes and interpreting geophysical observations. The laser-heated diamond anvil cell (DAC) is currently the only technique capable of routinely accessing the Earth's lower-mantle geotherm for experiments on non-metallic samples, but large temperature uncertainties and poor temperature stability limit the accuracy of measured data and prohibits analyses requiring long acquisition times. We have developed a novel internal resistive heating (IRH) technique for the DAC and demonstrate stable heating of non-metallic samples up to 3000K and 64GPa, as confirmed by in situ synchrotron x-ray diffraction and simultaneous spectroradiometric temperature measurement. The temperature generated in our IRH-DAC can be precisely controlled and is extremely stable, with less than 20K variation over several hours without any user intervention, resulting in temperature uncertainties an order of magnitude smaller than those in typical laser-heating experiments. Our IRH-DAC design, with its simple geometry, provides a new and highly accessible tool for investigating materials at extreme conditions. It is well suited for the rapid collection of high-resolution P-V-T data, precise demarcation of phase boundaries, and experiments requiring long acquisition times at high temperature. Our IRH technique is ideally placed to exploit the move toward coherent nano-focused x-ray beams at next-generation synchrotron sources.

Evidence of hydrogen-helium immiscibility at Jupiter-interior conditions.

The phase behaviour of warm dense hydrogen-helium (H-He) mixtures affects our understanding of the evolution of Jupiter and Saturn and their interior structures1,2. For example, precipitation of He from a H-He atmosphere at about 1-10 megabar and a few thousand kelvin has been invoked to explain both the excess luminosity of Saturn1,3, and the depletion of He and neon (Ne) in Jupiter's atmosphere as observed by the Galileo probe4,5. But despite its importance, H-He phase behaviour under relevant planetary conditions remains poorly constrained because it is challenging to determine computationally and because the extremes of temperature and pressure are difficult to reach experimentally. Here we report that appropriate temperatures and pressures can be reached through laser-driven shock compression of H2-He samples that have been pre-compressed in diamond-anvil cells. This allows us to probe the properties of H-He mixtures under Jovian interior conditions, revealing a region of immiscibility along the Hugoniot. A clear discontinuous change in sample reflectivity indicates that this region ends above 150 gigapascals at 10,200 kelvin and that a more subtle reflectivity change occurs above 93 gigapascals at 4,700 kelvin. Considering pressure-temperature profiles for Jupiter, these experimental immiscibility constraints for a near-protosolar mixture suggest that H-He phase separation affects a large fraction-we estimate about 15 per cent of the radius-of Jupiter's interior. This finding provides microphysical support for Jupiter models that invoke a layered interior to explain Juno and Galileo spacecraft observations1,4,6-8.

Elucidation of some solar parameters observed during solar cycles 21–24

Solar-terrestrial environment is manifested primarily by the physical conditions of the solar interior, solar atmosphere and eruptive solar plasma. Each parameter gives unique information about the Sun and its activity according to its defined characteristics. Hence the variability of solar parameters is of interest from the point of view of plasma dynamics on the Sun and into the interplanetary space as well as for the solar-terrestrial physics. In this study, we have analysed various solar and related parameters to examine the status of solar activity during solar cycles 21, 22, 23 and 24. The correlation coefficients of the linear regression of F10.7 cm index, Lyman alpha index, Mg II index, cosmic ray intensity, number of M & X class flares and coronal mass ejections (CMEs) occurrence rate versus sunspot number were analysed. A running cross-correlation method has been used to study the momentary relationship among the above mentioned solar activity parameters. Solar cycle 21 witnessed the highest value of correlation for F10.7 cm index, Lyman alpha index and number of M-class & X - class flares versus sunspot number among all the considered solar cycles which were about 0.979, 0.935 and 0.964 respectively. Solar cycle 22 recorded the highest correlation in case of Mg II index, A p index and CMEs occurrence rate versus sunspot number among all the considered solar cycles (0.964, 0.384 and 0.972 respectively). Solar cycle 23 and 24 did not witness any highest correlation compared to solar cycle 21 and 22. Further the record values (highest value compared to other solar cycles) of each solar activity parameters for each of the four solar cycles have been studied. Solar cycle 24 has no record text at all, this simply indicating that this cycle was a weakest cycle compared to the three previous ones. Thus in every domain solar 24 has been observed weaker in comparison of its three predecessors.

Effect of plasma screening on electron impact excitation and ionization of Fe16+ in a dense environment

ABSTRACT Electron impact excitation and ionization with atoms and ions within a dense plasma are fundamental microscopic processes that determine the ionization balance, physical properties (such as electron conductive opacity and thermal conductivity) and plasma formation and dynamics. While collision cross-sections and rates are well studied in dilute systems, similar investigations are scarce for dense plasmas under stellar interior conditions using an appropriate plasma-screening potential. Here we investigate the plasma-screening effect on the electron impact excitation and ionization cross-sections, effective collision strengths, and rate coefficients within plasmas under stellar interior conditions in a mass density range of 1–15.748 g cm−3 and a temperature range of 200–1000 eV. These investigations were carried out using our recently developed plasma-screening model, taking Fe16+ as an example. The results show that the cross-sections of the electron impact excitation are generally decreased, whereas they are always significantly increased for the collision ionization due to the plasma screening. In a plasma at a temperature of 200 eV and density of 15.748 g cm−3, the plasma screening causes a decrease in the excitation cross-section of 36 per cent for the dipole-allowed transition $2\mathrm{ s}^22\mathrm{ p}^6~^1\mathrm{ S}_0 \rightarrow 2\mathrm{ s}^22\mathrm{ p}^53\mathrm{ d}~^1\mathrm{ P}^o_1$ and of 50 per cent for the dipole-forbidden transition $2\mathrm{ s}^22\mathrm{ p}^6~^1\mathrm{ S}_0 \rightarrow 2\mathrm{ s}^22\mathrm{ p}^53\mathrm{ d}~^3\mathrm{ D}^o_1$. However, the collision ionization cross-section of a 2p electron from the ground level of Fe16+ is increased by 500 per cent and 100 per cent under an incident electron energy of 1500 and 10 000 eV, respectively. This results in the rate coefficient increasing by a factor of 18.5 at a temperature of 200 eV and density of 15.748 g cm−3.

Photosynthetic Responses of Anthurium × 'Red' under Different Light Conditions.

Light is an essential energy source for plant photosynthesis, although it can also be a stress-causing element. Therefore, the current research was aimed to compare photosynthetic responses of Anthurium × ‘Red’ leaves at different positions (bottom old leaf, 1; center mature leaf, 2; top expanded leaf, 3) established under three photosynthetic photon flux densities (PPFDs): 550 μmol·m−2·s−1 as high (H), 350 μmol·m−2·s−1 as medium (M), and 255 μmol·m−2·s−1 as low (L). After six months, all the replicates were relocated to interior rooms with a PPFD of 30 μmol·m−2·s−1. There were no significant differences in chlorophyll concentration of the old leaf among treatments, before (Day 0) and after shifting the plants to interior rooms (Day 30). The total chlorophyll concentrations of the mature and top leaves increased significantly. In greenhouse conditions, H and M treatments did not show any significant change for net photosynthetic rate (Pn) at various leaf positions. However, M2 exhibited an improved Pn in the interior conditions. Plants grown under M treatment were greener and had bigger leaves compared to other treatments. Our study reveals that Anthurium × ‘Red’ photosynthesis responses to different light conditions varied distinctly. However, M treatment can keep the plants looking green by accumulating enough energy for indoor conditions, and middle and lower leaves may be triggered to restore photosynthetic activity under low light or indoor conditions.

Web crippling design of lean duplex stainless steel tubular members under interior loading conditions

Numerical analysis and design of cold-formed lean duplex stainless steel (CFLDSS) tubular members undergoing web crippling are presented in this paper. The tubular members were subjected to the loading conditions of Interior-One-Flange (IOF), Interior-Two-Flange (ITF) and Interior Loading (IL). Finite element (FE) models were developed to simulate the members under these three interior loading conditions. The results obtained from the FE analysis were used to compare with test results in terms of failure modes, strengths and load-deformation curves. After successful verification, the FE models were employed for an extensive parametric study. The key parameters in the parametric study included the ratios of flat web height to thickness, load bearing length to web thickness, load bearing length to flat web height and section inner radius. The parametric study results together with the test results were used to compare with the nominal strengths predicted by using the current specifications (ASCE, AS/NZS, NAS and EC3), and the design equations in the literature. New sets of coefficients are proposed for the unified design equation in NAS and the direct strength method (DSM) for the web crippling design of CFLDSS tubular members. Overall, the modified design rules were able to provide more accurate predictions compared with the design rules in current specifications and literature. The results showed that the proposed design methods are suitable for the design of web crippling of CFLDSS tubular members under the IOF, ITF and IL conditions.

Variational interior and interface transmission conditions: multidomain mixed Darcy/Stokes control problems

Multidomain mixed pairs of coupled stationary constrained boundary value problems, are formulated variationally in frameworks of reflexive Banach spaces as macro-hybrid systems, and analyzed. Interior synchronizing and interface coupling transmission constraints are modeled in terms of Lagrange multipliers as solutions of dual variational subpotential maximal monotone inclusions. Existence and uniqueness results are established via resolvent fixed-point characterizations of the corresponding primal and dual macro-hybridized problems. Multimedia mixed mechanical subsurface-surface Darcy/Stokes incompressible flow coupled pairs with intrinsic distributed control constraints exemplify the general macro-hybrid mixed systems. Coupling dual-primal and primal-dual interface macro-hybrid mixed variational conditions are lastly developed and applied to the Darcy/Stokes multimedia pair model.

Degassing of volcanic extrusives on Mercury: Potential contributions to transient atmospheres and buried polar deposits

The surface of Mercury is dominated by extensive, widespread lava plains that formed early in its history. The emplacement of these lavas was accompanied by the release of magmatic volatiles, the bulk of which were lost to space via thermal escape and/or photodissociation. Here we consider the fate of these erupted volatiles by quantifying the volumes of erupted volcanic plains and estimating the associated masses of erupted volatiles. The concentrations and speciation of volatiles in Mercury's magmas are not known with certainty at this time, so we model a wide range of cases, based on existing experimental data and speciation models, at 3–7 log fO2 units below conditions determined by the iron-wüstite buffer. Cases range from relatively low gas content scenarios (total exsolved gas mass of 9×1015 kg) to high gas content scenarios (total exsolved gas = 5 × 1019 kg). We estimate that the average duration of a transient volcanic atmosphere resulting from a single eruption would be between ∼250 and ∼210,000 years, depending on the volume, degassed volatile content, and eruption rate of an individual eruption, as well as the fO2 conditions of the planet's interior. If a dense transient atmosphere was ever surface-bound long enough for the released volatiles to be transported to and cold-trapped at Mercury's polar regions, those trapped volatiles are predicted to be well-mixed with the regolith, and at least 16 m beneath the surface given regolith gardening rates. These volatiles would have a composition and age distinctly different from those of the H2O-ice deposits observed at the poles of Mercury today.

The sum theorem for maximal monotone operators in reflexive Banach spaces revisited

The goal of this note is to present a new shorter proof for the maximal monotonicity of the Minkowski sum of two maximal monotone multi-valued operators defined in a reflexive Banach space under the classical interiority condition involving their domains.

Short-term analysis of residential lighting: A pilot study

Lighting is one of the environmental elements that facilitates people to maintain their lives. With light people can collect visual cues about their environments in which they can perform visual tasks safely and comfortably. Exploring the lighting systems and conditions in residential interiors is important for introducing new concepts concerning human visual comfort. The study aimed to collect data and conduct a short-term analysis about residential lighting which will be a part of a more comprehensive research. The study focused on day- and artificial lighting systems, conditions and people’s assessments in interiors of residential buildings. An internet-based survey was distributed in July-August 2020 through Google Survey across Poland, Turkey, the U.K. and Sweden in the native languages of each country. 29 adult females and 31 adult males voluntarily participated in the present study. The study identified several interconnected factors related to residential lighting and explored them in detail. Large percentage of the respondents were satisfied or very satisfied with daylighting quality in summer (86.7%) and artificial lighting quality (78.4%) in their living areas. The amount and uniformity of lighting were the most effective cues connected with the respondents’ satisfaction. Reasonable and promising outcomes that were found can be used in generating new and comprehensive data about lighting quality in residential buildings.

Morpho-physiological features of Stephanotis floribunda inconditions of greenhouse culture

Stephanotis floribunda Brongn. is an ornamental pot-plant characterized with intensive growth, profuse flowering, stability in interior conditions. We studied the growth and developmental rhythm of the shoot system of the experimental plant, investigated its biomorphological features, compared the physiological and biochemical characteristics of the assimilating organs of Stephanotis floribunda during the growing season in phases: budding, mass flowering, flowering end, single flowering, slow growth and relative peace. The system of stephanotis shoots is characterized by a plagiotropic growth direction and all its vegetative-generative areas are structurally homogeneous. Due to its ability to take root in each node, the structural unit – metamer – retains autonomy and is able to restore the entire individual. The indicators of the pigment composition throughout the whole observation period indicate the stability of the photosynthetic system, and confirm the significant adaptation potential of Stephanotis floribunda in protected ground conditions.

Superionic iron oxide–hydroxide in Earth’s deep mantle

Water ice becomes a superionic phase under the high pressure and temperature conditions of deep planetary interiors of ice planets such as Neptune and Uranus, which affects interior structures and generates magnetic fields. The solid Earth, however, contains only hydrous minerals with a negligible amount of ice. Here we combine high pressure and temperature electrical conductivity experiments, Raman spectroscopy and first-principles simulations to investigate the state of hydrogen in the pyrite-type FeO2Hx (x ≤ 1), which is a potential H-bearing phase near the core–mantle boundary. We find that when the pressure increases beyond 73 GPa at room temperature, symmetric hydroxyl bonds are softened and the H+ (or proton) becomes diffusive within the vicinity of its crystallographic site. Increasing temperature under pressure, the diffusivity of hydrogen is extended beyond the individual unit cell to cover the entire solid, and the electrical conductivity soars, indicating a transition to the superionic state, which is characterized by freely moving protons and a solid FeO2 lattice. The highly diffusive hydrogen provides fresh transport mechanisms for charge and mass, which dictate the geophysical behaviours of electrical conductivity and magnetism, as well as geochemical processes of redox, hydrogen circulation and hydrogen isotopic mixing in Earth’s deep mantle.

A Pattern Language for Social Field Shifts

The complex systemic issues of today, including climate change, racism, social inequality, mental health crisis, call for new ways of engaging the heart (feeling), mind (thinking), and will (doing) to actually change deep-rooted behaviors. To develop these new ways of engaging, one must learn how to cultivate first, one’s interior condition (the inner place from which we operate) and second, one's capacities to co-create with others the exterior conditions for healthy social relationships. In this paper, we claim that by living in a body we are embodied and that wisdom lives in a holistic knowing that includes embodied intelligence. We argue that to address the complex challenges of our times, we must cultivate embodied and perceptual capacities and a language for our embodied experience(s). Over three years of workshops with advanced practitioners of an embodied practice called Social Presencing Theater (SPT), we used embodied activities and design prompts (drawing, photo, video) to surface and make visible social patterns. This has led us to develop a language in the context of social systems change, in particular of social field shifts (i.e., transformations in the relational and felt qualities of our social systems). Through this paper we aim to contribute to social field research by proposing an embodied, visual, and verbal language for social groups to describe and reflect on social field shifts, made up of two parts: first, an aesthetic language to describe social field qualities; and second, three families of social field archetypes to describe social fields.

Multishock to Quasi-Isentropic Compression of Dense Gaseous Deuterium-Helium Mixtures up to 120GPa: Probing the Sound Velocities Relevant to Planetary Interiors.

Shock reverberation compression experiments on dense gaseous deuterium-helium mixtures are carried out to provide thermodynamic parameters relevant to the conditions in planetary interiors. The multishock pressures are determined up to 120GPa and reshock temperatures to 7400K. Furthermore, the unique compression path from shock-adiabatic to quasi-isentropic compressions enables a direct estimation of the high-pressure sound velocities in the unexplored range of 50-120GPa. The equation of state and sound velocity provide particular dual perspectives to validate the theoretical models. Our experimental data are found to agree with several equation of state models widely used in astrophysics within the probed pressure range. The current data improve the experimental constraints on sound velocities in the Jovian insulating-to-metallic transition layer.

A divergence-free generalized moving least squares approximation with its application

An approximation based on moving least squares for vector-valued functions satisfying the divergence-free property was employed in [67] by Trask, Maxey, and Hu. They changed the traditional polynomial bases in moving least squares approximation to the vector-valued polynomial basis functions satisfying the divergence-free property for constructing a new vector-valued approximation. In this paper, we adopt [67], but we consider another approach, i.e., a direct method based on the generalized moving least squares (GMLS) approximation for vector-valued functions, which satisfy the divergence-free property. This GMLS approximation produces diffuse or uncertain derivatives for each component of the proposed vector-valued approximation satisfying the divergence-free property. Using the new approach, the linear functionals such as the derivatives act only on each row of the vector-valued polynomial basis functions, which reduces the computational cost comparing with the divergence-free moving least squares approximation. The pointwise error estimates of the presented approximation are obtained for the bounded sub-domains in Rd(d≥2) with an interior cone condition. Some numerical results are provided to confirm the obtained theoretical results. As an application, the Cahn-Hilliard-Hele-Shaw (CHHS) equation is solved numerically via a stabilized semi-implicit scheme in time that holds the mass conservative and energy dissipative properties and also the GMLS approximation in space. Besides, the developed vector-valued approximation has been used to compute the Leray-Helmholtz projection of the advective velocity.